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![Recent Advances in Signal Processing
4
utilizes directly the intensity information in the image pixels, without searching for specific
visual features.
In general a parametric model for the two-dimensional mapping function that overlaps an
"input" image over a "reference" image is assumed. Let us denote such mapping function by
t(x; p) = [tx(x; p) ty(x; p)]t, where x = [x y]t stands for the coordinates of an image pixel,
and p denotes the parameter vector of the transformation. Denoting the "input" and "refer-
ence" images by h and g respectively, the objective of an image based registration approach
is to estimate the parameter vector p that minimizes a cost function (e.g., the sum of square
differences) between the transformed input image h(t(x; p)) and the reference image g(x).
The minimization of the cost function, can be achieved in various ways. A trivial approach
would be to adopt an exhaustive search among all feasible solutions by calculating the cost
function at all possible values of the parameter vector. Although this method ensures the
discovery of the global optimum, it is usually avoided due to its tremendous complexity.
To improve the efficiency several alternatives to the exhaustive search technique have been
developed by reducing the searching space at the risk of losing the global optimum, e.g.,
logarithmic search, three-step search, etc, (see Wang et al. (2002)). Another category of image
based registration approaches, starting with the work of Lucas & Kanade (1981), and known
also as gradient-based approaches, assumes that an approximation to image derivatives can
be consistently estimated, such that the minimization of the cost function can be achieved
by applying a gradient-descent technique (see also Baker & Matthews (2004); Thevenaz &
Unser (1998)). An important efficiency improvement, for Lucas-Kanade algorithm, has been
proposed in Baker & Matthews (2004), under the name of "Inverse Compositional Algorithm"
(ICA). The improvement results from the fact that the Hessian matrix of the cost function,
needed in the optimization process, is not calculated in each iteration, but only once in a pre-
computation phase.
In this work we propose an additional improvement to gradient-based methods, that consists
of simplifying the repetitive image warping and interpolation operations that are required
during the iterative minimization of the cost function. Our presentation starts by introducing
an image descriptor in Section 2.1, that is less illumination dependent than the intensity com-
ponent. Next, we present our registration algorithm in Section 2.2, that is based on matching
the proposed image descriptors of the two images instead their intensity components.
2.1 Preprocessing
Most of the registration methods proposed in the literature are based on matching the inten-
sity components of the given images. However, there are also situations when the intensity
components do not match. The most common such cases are those in which the two images
have been captured under different illumination conditions, or with different exposures.
In order to cope with such cases we propose a simple preprocessing step aiming to extract an
illumination invariant descriptor from the intensity component of each image. Denoting by
H(x) the intensity value in the pixel x, and with avg(H) the average of all intensity values
in the image, we first calculate H̄(x) = H(x)/avg(H), in order to gain more independence
from the global scene illumination. Next, based on the gradient of H̄ we calculate Hg(x) =
∣H̄x(x)∣ + ∣H̄y(x)∣ in each pixel, and med(Hg) as the median value of Hg(x) over the entire
image.](https://image.slidesharecdn.com/1132368-250521160742-103f5a0c/85/Recent-Advances-In-Signal-Processing-Ashraf-A-Zaher-22-320.jpg)
![Digital Image Stabilization 5
Finally, the actual descriptor that we are using in the registration operation is given by the
following binary image
h(x) =
{
1 if Hg(x) > med(Hg)
0 otherwise
(1)
2.2 Registration algorithm
In the following we describe an image based registration method that is using a multi-
resolution coarse to fine strategy. Typically in such algorithm, at each iteration step one of
the images should be warped in accordance to the parameters estimated so far. In our method
this warping operation is highly simplified on the expense of increase memory usage.
The levels of the multi-resolution representation are over-sampled, and they are obtained
by iteratively smoothing the original image descriptor h, such that to obtain smoother and
smoother versions of it. Let h̃ℓ denotes the smoothed image resulted after ℓ-th low-pass filter-
ing iterations (h̃0 = h). The smoothed image at next iteration can be calculated by applying
one-dimensional filtering along the image rows and columns as follows:
h̃ℓ+1 (x, y) = ∑
r
wr ∑
c
wch̃ℓ
(
x − 2ℓ
c, y − 2ℓ
r
)
, (2)
where wk are the taps of a low-pass filter.
The registration approach takes advantage of the fact that each decomposition level (h̃ℓ) is
over-sampled, and hence it can be reconstructed by a subset of its pixels. This property allows
to enhance the efficiency of the registration process by using only a subset of the pixels in the
registration algorithm. The advantage offered by the availability of over-sampled decompo-
sition level, is that the set of pixels that can be used in the registration is not unique. A broad
range of geometrical transformations can be approximated by simply choosing a different set
of pixels to describe the sub-sampled image level. In this way, the over-sampled image level
is regarded as a "reservoir of pixels" for different warped sub-sampled versions of the image,
which are needed at different stages in the registration algorithm.
Let xn,k = [xn,k yn,k]t, for n, k integers, denote the coordinates of the selected pixels into the
smoothed image (h̃ℓ). A low-resolution version of the image (ĥℓ) can be obtained by col-
lecting the values of the selected pixels: ĥℓ(n, k) = h̃ℓ(xn,k). Moreover, given an invertible
geometrical transformation function t(x; p), the warping version of the low resolution image
can be obtained more efficiently by simply selecting another set of pixels from the area of the
smoothed image, rather than warping and interpolating the low-resolution image ĥℓ. This is:
ĥ′
ℓ(n, k) = h̃ℓ(x′
n,k), where x′
n,k = round
(
t−1(xn,k; p)
)
.
The process described above is illustrated in Fig.3, where the images shown on the bottom
row represent two low-resolutions warped versions of the original image (shown in the top-
left corner). The two low-resolution images are obtained by sampling different pixels from
the smoothed image (top-right corner) without interpolation.
The registration method used in our approach is presented in Algorithm 1. The algorithm
follows a coarse to fine strategy, starting from a coarse resolution level and improving the pa-
rameter estimate with each finer level, as details in the Algorithm 2. The proposed algorithm
relies on matching image descriptors (1) derived from each image rather than image intensity
components.
Algorithm 2 presents the registration parameter estimation at one resolution level. In this
algorithm, the constant N0, specifies the number of iterations the algorithm is performing](https://image.slidesharecdn.com/1132368-250521160742-103f5a0c/85/Recent-Advances-In-Signal-Processing-Ashraf-A-Zaher-23-320.jpg)
![Recent Advances in Signal Processing
6
50 100 150 200 250
50
100
150
200
250
50 100 150 200 250
50
100
150
200
250
5 10 15 20 25
5
10
15
20
25
5 10 15 20 25
5
10
15
20
25
Fig. 3. Low-resolution image warping by re-sampling an over-sampled image decomposition
level.
Algorithm 1 Global image registration
Input: the input and reference images plus, if available, an initial guess of the parameter
vector p = [p1 p2 ⋅ ⋅ ⋅ pK]t.
Output: the parameter vector that overlaps the input image over the reference image.
1- Calculate the descriptors (1) for input and reference images, denoted here by h and g,
respectively.
2- Calculate the decomposition levels of the two image descriptors {h̃ℓ, g̃ℓ ∣ ℓmin ≤ ℓ ≤
ℓmax}.
3- For each level ℓ between ℓmax and ℓmin, do Algorithm 2.
after finding a minima of the error function. This is set in order to reduce the chance of ending
in a local minima. As shown in the algorithm the number of iterations is reset to N0, every
time a new minima of the error function is found. The algorithm stops only if no other minima
is found in N0 iterations. In our experiments a value N0 = 10 has been used.](https://image.slidesharecdn.com/1132368-250521160742-103f5a0c/85/Recent-Advances-In-Signal-Processing-Ashraf-A-Zaher-24-320.jpg)
![Digital Image Stabilization 7
Algorithm 2 Image registration at one level
Input: the ℓ-th decomposition level of the input and reference images (h̃ℓ, g̃ℓ), plus the
parameter vector p = [p1 p2 ⋅ ⋅ ⋅ pK]t estimated at the previous coarser level.
Output: a new estimate of the parameter vector pout that overlaps h̃ℓ over g̃ℓ.
Initialization: set minimum matching error Emin = ∞, number of iterations Niter = N0
1- Set the initial position of the sampling points xn,k in the vertex of a rectangular lattice
of period D = 2ℓ, over the area of the reference image g̃ℓ.
2- Construct the reference image at this level: ĝ(n, k) = g̃ℓ(xn,k).
3- For each parameter pi of the warping function calculate the image
Ji(n, k) = ĝx(n, k)
∂tx(x; 0)
∂pi
+ ĝy(n, k)
∂ty(x; 0)
∂pi
where ĝx, ĝy denote a discrete approximation of the gradient components of the reference
image.
4- Calculate the first order approximation of the K × K Hessian matrix, whose element
(i, j) is given by:
H(i, j) = ∑
n,k
Ji(n, k)Jj(n, k)
5- Calculate a K × K updating matrix U, as explain in the text.
Iterations: while Niter > 0
6- Construct the warped low-resolution input image in accordance to the warping param-
eters estimated so far: ĥ(n, k) = h̃ℓ(round
(
t−1(xn,k; p)
)
).
7- Determine the overlapping area between ĥ and ĝ, as the set of pixel indices Ψ such that
any pixel position (n, k) ∈ Ψ is located inside the two images.
8- Calculate the error image e(n, k) = ĥ(n, k) − ĝ(n, k), for any (n, k) ∈ Ψ.
9- Calculate a smooth version ẽ of the error image by applying a 2 × 2 constant box filter,
and determine total error E = ∑(n,k)∈Ψ ∣ẽ(n, k)∣.
10- If E ≥ Emin then Niter = Niter − 1, otherwise update Emin = E, Niter = N0, and
pout = p.
11- Calculate the K × 1 vector q, with q(i) = ∑(n,k)∈Ψ ẽ(n, k)Ji(n, k).
12- Update the parameter vector p = p + Uq
The parameter update (i.e., line 12 in Algorithm 2) makes use of an updating matrix U calcu-
lated in step 5 of the algorithm. This matrix depends of the functional form of the geometrical
transformation assumed between the two images, t(x; p). For instance, in case of affine trans-](https://image.slidesharecdn.com/1132368-250521160742-103f5a0c/85/Recent-Advances-In-Signal-Processing-Ashraf-A-Zaher-25-320.jpg)
![Recent Advances in Signal Processing
8
formation
t(x; p) =
[
(1 − p3)x + p4y + p1
p5x + (1 − p6)y + p2
]
, (3)
the parameter update matrix is
U = diag (D, D, 1, 1, 1, 1) H−1
, (4)
whereas in case of a projective transformation
t(x; p) =
[
(1 − p3)x + p4y + p1
p5x + (1 − p6)y + p2
]
/(p7x + p8y + 1), (5)
we have
U = diag (D, D, 1, 1, 1, 1, 1/D, 1/D) H−1
. (6)
In our implementation of multi-resolution image decomposition (2), we used a symmetric
filter w of size 3, whose taps are respectively w−1 = 1/4, w0 = 1/2, and w1 = 1/4. Also,
in order to reduce the storage space the first level of image decomposition (i.e., h̃1), is sub-
sampled by 2, such that any higher decomposition level is half the size of the original image.
3. Fusion of multiple images
The pixel brightness delivered by an imaging system is related to the exposure time through
a non-linear mapping called "radiometric response function", or "camera response function"
(CRF). There are a variety of techniques (e.g., Debevec & Malik (1997); Mitsunaga & Nayar
(1999)) that can be used for CRF estimation. In our work we assume that the CRF function of
the imaging system is known, and based on that we can write down the following relation for
the pixel brightness value:
I(x) = CRF (g(x)∆t) (7)
where x = [x y]T denotes the spatial position of an image pixel, I(x) is the brightness value
delivered by the system, g(x) denotes the irradiance level caused by the light incident on the
pixel x of the imaging sensor, and ∆t stands for the exposure time of the image.
Let Ik, for k ∈ {1, . . . , K} denote the K observed image frames whose exposure times are
denoted by ∆tk. A first step in our algorithm is to convert each image to the linear (irradiance)
domain based on knowledge about the CRF function, i.e.,
gk(x) = (1/∆tk) CRF−1
(Ik(x)) , for all k ∈ {1, . . . , K}. (8)
We assume the following model for the K observed irradiance images:
gk(x) = fk(x) + nk(x), (9)
where where x = [x y]T denotes the spatial position of an image pixel, gk is the k-th observed
image frame, nk denotes a zero mean additive noise, and fk denotes the latent image of the
scene at the moment the k-th input frame was captured. We emphasize the fact that the scene
may change between the moments when different input frames are captured. Such changes
could be caused by unwanted motion of the camera and/or by the motion of different objects
in the scene. Consequently, the algorithm can provide a number of K different estimates of
the latent scene image each of them corresponding to a different reference moment.](https://image.slidesharecdn.com/1132368-250521160742-103f5a0c/85/Recent-Advances-In-Signal-Processing-Ashraf-A-Zaher-26-320.jpg)
![Digital Image Stabilization 9
In order to preserve the consistency of the scene, we select one of the input images as reference,
following to aim for improving the selected image based on the visual data available in all
captured images. In the following, we denote by gr, (r ∈ {1, . . . , K}) the reference image
observation, and hence the objective of the algorithm is to recover an estimate of the latent
scene image at moment r, i.e., f = fr.
The restoration process is carried out based on a spatiotemporal block processing. Assuming
a division of gr in non-overlapping blocks of size B × B pixels, the restored version of each
block is obtained as a weighted average of all blocks located in a specific search range, inside
all observed images.
Let XB
x denote the sub-set of spatial locations included into a block of B × B pixels centered in
the pixel x, i.e.:
XB
x =
{
y ∈ Ω ∣ [−B − B]T
< 2 (y − x) ≤ [B B]T
}
, (10)
where the inequalities are componentwise, and Ω stands for the image support. Also, let
g(XB
x ) denote the B2 × 1 column vector comprising the values of all pixels from an image g
that are located inside the block XB
x .
The restored image is calculated block by block as follows
ˆ
f (XB
x ) =
1
Z
K
∑
k=1
∑
y∈XS
x
wk (x, y) gk(XB
y ), for all XB
x , (11)
where Z = ∑K
k=1 ∑y∈XS
x
wk (x, y), is a normalization value, XS
x denotes the spatial search range
of size S × S centered in x, and wk (x, y) is a scalar weight value assigned to an input block XB
y
from image gk.
The weight values are emphasizing the input blocks that are more similar with the reference
block. Note that, at the limit, by considering only the most similar such block from each input
image we obtain the block corresponding to the optical flow between the reference image and
that input image, as in Tico & Vehviläinen (2007b). In such a case the weighted average (11)
comprises only a small number of contributing blocks for each reference block. If more com-
putational power is available, we can chose the weight values such that to use more blocks
for the restoration of each reference block, like for instance in the solution presented in Tico
(2008a), where the restoration of each reference block is carried out by considering all visu-
ally similar blocks found either inside the reference image or inside any other input image.
Although the use of block processing is more efficient for large images, it might create arti-
facts in detailed image areas. In order to cope with this aspect, the solution presented in Tico
(2008a), proposes a mechanism for adapting the block size to the local image content, by us-
ing smaller blocks in detail areas and larger blocks in smooth areas of the image. We conclude
this section by summarizing the operations of a multi-frame image stabilization solutions in
Algorithm 3.](https://image.slidesharecdn.com/1132368-250521160742-103f5a0c/85/Recent-Advances-In-Signal-Processing-Ashraf-A-Zaher-27-320.jpg)
![About array processing methods for image segmentation 35
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Recent Advances In Signal Processing Ashraf A Zaher
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- 8. Published by In-Teh In-Teh Olajnica19/2, 32000 Vukovar, Croatia Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the In-Teh, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2009 In-teh www.intechweb.org Additional copies can be obtained from: publication@intechweb.org First published November 2009 Printed in India Technical Editor: Maja Jakobovic Recent Advances in Signal Processing, Edited by Ashraf A. Zaher p. cm. ISBN 978-953-307-002-5
- 9. V Preface The signal processingtask is a very critical issue in the majority of new technological in- ventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This was mainly due to the revolutionary advances in the digital technology and the ability to effectively use digital signal processing (DSP) that rely on the use of very large scale integrated technologies and efficient computational methods such as the fast Fourier transform (FFT). This trend is expected to grow exponentially in the future, as more and more emerging technologies are revealed in the fields of digital computing and software development. It is still an extremely skilled work to properly design, build and implement an effective sig- nal processing tool able to meet the requirements of the increasingly demanding and sophis- ticated modern applications. This is especially true when it is necessary to deal with real-time applications of huge data rates and computational loads. These applications include image compression and encoding, speech analysis, wireless communication systems, biomedical real-time data analysis, cryptography, steganography, and biometrics, just to name a few. Moreover, the choice between whether to adopt a software or hardware approach, for imple- menting the application at hand, is considered a bottleneck. Programmable logic devices, e.g. FPGAs provide an optimal compromise, as the hardware configuration can be easily tailored using specific hardware descriptive languages (HDLs). This book is targeted primarily toward both students and researchers who want to be ex- posed to a wide variety of signal processing techniques and algorithms. It includes 27 chap- ters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, commu- nication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another with- out losing continuity. Each chapter provides a comprehensive survey of the subject area and terminates with a rich list of references to provide an in-depth coverage of the application at hand. Understanding the fundamentals of representing signals and systems in both time, spa- tial, and frequency domains is a prerequisite to read this book, as it is assumed that the reader is familiar with them. Knowledge of other transform methods, such as the Laplace transform
- 10. VI and the Z-transform,along with knowledge of some computational intelligence techniques is an assist. In addition, experience with MATLAB programming (or a similar tool) is useful, but not essential. This book is application-oriented and it mainly addresses the design, imple- mentation, and/or the improvements of existing or new technologies, and also provides some novel algorithms either in software, hardware, or both forms. The reported techniques are based on time-domain analysis, frequency-domain analysis, or a hybrid combination of both. This book is organized as follows. The first 14 chapters investigate applications in the field of image processing, the next six chapters address applications in speech and audio processing, and the last seven chapters deal with applications in communication systems, real-time data handling, and interactive educational packages, respectively. There is a great deal of overlap between some of the chapters, as they might be sharing the same theory, application, or ap- proach; yet, we chose to organize the chapter into the following five sections: I. Image Processing: This section contains 14 chapters that explore different applications in the field of image pro- cessing. These applications cover a variety of topics related to segmentation, encoding, resto- ration, steganography, and denoising. Chapters (1) to (14) are arranged into groups based on the application of interest as explained in the following table: Chapter(s) Main topic (application) 1 – 3 Image segmentation and encoding 4 – 6 Medical applications 7 & 8 Data hiding 9 & 10 Image classification 11& 12 Biometric applications 13 & 14 Noise suppression Chapter (1) proposes a software approach to image stabilization that depends on two conse- quent steps of global image registration and image fusion. The improved reliability and the reduced size and cost of this approach make it ideal for small mobile devices. Chapter (2) investigates contour retrieval in images via estimating the parameters of rectilinear or circular contours as a source localization problem in high-resolution array processing. It presents a subspace-based line detection algorithm for the estimation of rectilinear contours based on signal generation upon a linear antenna. Chapter (3) proposes a locally adaptive resolution (LAR) codec as a contribution to the field of image compression and encoding. It focuses on a few representative features of the LAR technology and its preliminary associated perfor- mances, while discussing their potential applications in different image-related services. Chapter (4) uses nonlinear locally adaptive transformations to perform image registration with application to MRI brains scan. Both parametric and nonparametric transformations, along with the use of multi-model similarity measures, are used to robustify the results to
- 11. VII tissue intensity variations.Chapter (5) describes a semi-automated segmentation method for dynamic contrast-enhanced MRI sequences for renal function assessment. The superiority of the proposed method is demonstrated via testing and comparing it with manual segmenta- tion by radiologists. Chapter (6) uses a hybrid technique of motion estimation and segmenta- tion that are based on variational techniques to improve the performance of cardiac motion application in indicating heart diseases. Chapter (7) investigates the problem of restricting color information for images to only au- thorized users. It surveys some of the reported solutions in the literature and proposes an improved technique to hide a 512-color palette in an 8-bit gray level image. Chapter (8) in- troduces a novel application of the JPEG2000-based information hiding for synchronized and scalable 3D visualization. It also provides a compact, yet detailed, survey of the state of the art techniques in the field of using DWT in image compression and encoding. Chapter (9) uses a content-based image-retrieval technique to validate the results obtained from defects-detection algorithms, in Ad-hoc features, to find similar images suffering from the same defects in order to classify the questioned image as defected or not. Chapter (10) explores a novel approach for automatic crack detection and classification for the purpose of roads maintenance and estimating pavement surface conditions. This approach relies on image processing and pattern recognition techniques using a framework based on local sta- tistics, computed over non-overlapping image regions. Chapter (11) proposes a robust image segmentation method to construct a contact-free hand identification system via using infrared illumination and templates that guide the user in or- der to minimize the projective distortions. This biometric identification system is tested on a real-world database, composed by 102 users and more than 4000 images, resulting in an EER of 3.2%. Chapter (12) analyzes eye movements of subjects when looking freely at dynamic stimuli such as videos. This study uses face detection techniques to prove that faces are very salient in both static and dynamic stimuli. Chapter (13) reports the use of specialized denoising algorithms that deal with correlated noise in images. Several useful noise estimation techniques are presented that can be used when creating or adapting a white noise denoising algorithm for use with correlated noise. Chapter (14) presents a novel technique that estimates and eliminates additive noise inherent in images acquired under incoherent illumination. This technique combines the two methods of scatter plot and data masking to preserve the physical content of polarization-encoded images. II. Speech/Audio Processing: This section contains six chapters that explore different applications in the field of speech and audio processing. These applications cover a variety of topics related to speech analysis, enhancement of audio quality, and classification of both audio and speech. Chapters (15) to (20) are arranged into groups based on the application of interest as explained in the follow- ing table:
- 12. VIII Chapter(s) Main topic(application) 15 & 16 Speech/audio enhancement 17 & 18 Biometric applications 19 & 20 Speech/audio analysis Chapter (15) proposes an improved iterative Wiener filter (IWF) algorithm based on the time-varying complex auto regression (TV-CAR) speech analysis for enhancing the quality of speech. The performance of the proposed system is compared against the famous linear predictive coding (LPC) method and is shown to be superior. Chapter (16) introduces a ro- bust echo detection algorithm in mobile phones for improving the calls quality. The structure for the echo detector is based on comparison of uplink and downlink pitch periods. This algorithm has the advantage of processing adaptive multi-rate (AMR) coded speech signals without decoding them first and its performance is demonstrated to be satisfactory. Chapter (17) investigates the problem of voice/speaker recognition. It compares the effective- ness of using a combination of vector quantization (VQ) and different forms for the Mel fre- quency cepstral coefficients (MFCCs) when using the Gaussian mixture model for modeling the speaker characteristics. Chapter (18) deals with issues, related to processing and mining of specific speech information, which are commonly ignored by the mainstream research in this field. These issues focus on speech with emotional content, effects of drugs and Alcohol, speakers with disabilities, and various kinds of pathological speech. Chapter (19) uses narrow-band filtering to construct an estimation technique of instantaneous parameters used in sinusoidal modeling. The proposed method utilizes pitch detection and estimation for achieving good analysis of speech signals. Chapter (20) conducts an experi- mental study on 420 songs from four different languages to perform statistical analysis of the music information that can be used as prior knowledge in formulating constrains for music information extraction systems. III. Communication Systems: This section contains three chapters that deal with the transmission of signals through public communication channels. Chapters (21) to (23) discuss the problems of modeling and simula- tion of multi-input multi-output wireless channels, multi-antenna receivers, and chaos-based cryptography, respectively. Chapter (21) discusses how to construct channel simulators for multi-input multi-output (MIMO) communication systems for testing physical layer algo- rithms such as channel estimation. It also presents the framework, techniques, and theories in this research area. Chapter (22) presents a new approach to the broadcast channel problem that is based on combining dirty-paper coding (DPC) with zero-forcing (ZF) precoder and optimal beamforming design. This approach can be applied to the case when several antennas coexist at the receiver. It also introduces an application that deals with the cooperation design in wireless sensor networks with intra and intercluster interference. Chapter (23) investigates three important steps when establishing a secure communication system using chaotic sig- nals. Performing fast synchronization, identifying unknown parameters, and generating ro- bust cryptography are analyzed. Different categories of systems are introduced and real-time implementation issues are discussed.
- 13. IX IV. Time-series Processing: Thissection contains three chapters that deal with real-time data handling and processing. These data can be expressed as functions of time, sequence of images, or readings from sen- sors. It provides three different applications. Chapter (24) introduces an application, which is based on the fusion of electronecephalography (EEG) and functional magnetic resonance im- aging (fMRI), for the detection of seizure. It proposes a novel constrained spatial independent component analysis (ICA) algorithm that outperforms the existing unconstrained algorithm in terms of estimation error and closeness between the component time course and the seizure EEG signals. Chapter (25) introduces the design and implementation of a real-time measure- ment system for estimating the air parameters that are vital for effective and reliable flights. The proposed system is installed in the cockpit of the aircraft and uses two embedded PCs and four FPGA signal processing boards. It utilizes laser beams for estimating the air param- eters necessary for the safety of the flight. Chapter (26) discusses the performance of the target signal port-starboard discrimination for underwater towed multi-line arrays that have typical applications in military underwater surveillance and seismic exploring V. Educational Systems: Chapter (27) introduces an open source software package that can be used as an educational tool for teaching signal processing in a variety of fields including image and audio processing. It provides an interactive environment that is easy to use with GUI and web interface that is XML-based. This package can be used as an alternative to other existing packages including J-DSP, Simulink and SciLab. November 2009 Ashraf A. Zaher
- 14.
- 15. XI Contents Preface V 1. DigitalImage Stabilization 001 Marius Tico 2. About array processing methods for image segmentation 015 J. Marot, C. Fossati and Y. Caulier 3. Locally Adaptive Resolution (LAR) codec 037 François Pasteau, Marie Babel, Olivier Déforges, Clément Strauss and Laurent Bédat 4. Methods for Nonlinear Intersubject Registration in Neuroscience 049 Daniel Schwarz and Tomáš Kašpárek 5. Functional semi-automated segmentation of renal DCE-MRI sequences using a Growing Neural Gas algorithm 069 Chevaillier Beatrice, Collette Jean-Luc, Mandry Damien and Claudon 6. Combined myocardial motion estimation and segmentation using variational techniques 081 N. Carranza-Herrezuelo, A. Bajo, C. Santa-Marta, G. Cristóbal and A. Santos, M.J. Ledesma-Carbayo 7. Protecting the color information by hiding it 101 Marc CHAUMONT and William PUECH 8. JPEG2000-Based Data Hiding and its Application to 3D Visualization 123 Khizar Hayat, William Puech and Gilles Gesquière 9. Content-Based Image Retrieval as Validation for Defect Detection in Old Photos 147 Edoardo Ardizzone, Haris Dindo and Giuseppe Mazzola 10. Supervised Crack Detection and Classification in Images of Road Pavement Flexible Surfaces 159 Henrique Oliveira and Paulo Lobato Correia
- 16. XII 11. Contact-free handbiometric system for real environments based on geometric features 185 Aythami Moralesand Miguel A. Ferrer 12. Gaze prediction improvement by adding a face feature to a saliency model 195 MARAT Sophie, GUYADER Nathalie and PELLERIN Denis 13. Suppression of Correlated Noise 211 Jan Aelterman, Bart Goossens, Aleksandra Pizurica and Wilfried Philips 14. Noise Estimation of Polarization-Encoded Images by Peano-Hilbert Fractal Path 237 Samia Ainouz-Zemouche and Fabrice Mériaudeau 15. Speech Enhancement based on Iterative Wiener Filter using Complex LPC Speech Analysis 251 Keiichi Funaki 16. Detection of echo generated in mobile phones 267 Tõnu Trump 17. Application of the Vector Quantization Methods and the Fused MFCC-IMFCC Features in the GMM based Speaker Recognition 281 Sheeraz Memon, Margaret Lech, Namunu Maddage and Ling He 18. Information Mining from Speech Signal 297 Milan Sigmund 19. Estimation of the instantaneous harmonic parameters of speech 321 Elias Azarov and Alexander Petrovsky 20. Music Structure Analysis Statistics for Popular Songs 345 Namunu C. Maddage, Li Haizhou and Mohan S. Kankanhalli 21. MIMO Channel Modeling and Simulation 367 R. Parra-Michel, A. Alcocer-Ochoa, A. Sanchez-Hernandez and Valeri Kontorovich 22. On the role of receiving beamforming in transmitter cooperative communications 395 Santiago Zazo, Ivana Raos and Benjamín Béjar 23. Robust Designs of Chaos-Based Secure Communication Systems 415 Ashraf A. Zaher 24. Simultaneous EEG-fMRI Analysis with Application to Detection of Seizure Signal Sources 441 Min Jing and Saeid Sanei
- 17. XIII 25. Real-Time SignalAcquisition, High Speed Processing and Frequency Analysis in Modern Air Data Measurement Instruments 459 Theodoros Katsibas, Theodoros Semertzidis, Xavier Lacondemine and Nikos Grammalidis 26. Performance analysis of port-starboard discrimination for towed multi-line array 481 Biao Jiang 27. Audio and Image Processing Easy Learning for Engineering Students using EasyPAS Tool 501 Javier Vicente, Begoña García, Amaia Méndez and Ibon Ruiz
- 19. Digital Image Stabilization1 0 Digital Image Stabilization Marius Tico Nokia Research Center Palo Alto, CA, USA 1. Introduction The problem of image stabilization dates since the beginning of photography, and it is basi- cally caused by the fact that any known image sensor needs to have the image projected on it during a period of time called integration time. Any motion of the camera during this time causes a shift of the image projected on the sensor resulting in a degradation of the final image, called motion blur. The ongoing development and miniaturization of consumer devices that have image acquisi- tion capabilities increases the need for robust and efficient image stabilization solutions. The need is driven by two main factors: (i) the difficulty to avoid unwanted camera motion when using a small hand-held device (like a camera phone), and (ii) the need for longer integration times due to the small pixel area resulted from the miniaturization of the image sensors in conjunction with the increase in image resolution. The smaller the pixel area the less pho- tons/second could be captured by the pixel such that a longer integration time is needed for good results. It is of importance to emphasize that we make a distinction between the terms "digital image stabilization" and "digital video stabilization". The latter is referring to the process of eliminat- ing the effects of unwanted camera motion from video data, see for instance Erturk & Dennis (2000); Tico & Vehviläinen (2005), whereas digital image stabilization is concerned with cor- recting the effects of unwanted motions that are taking place during the integration time of a single image or video frame. The existent image stabilization solutions can be divided in two categories based on whether they are aiming to correct or to prevent the motion blur degradation. In the first category are those image stabilization solutions that are aiming for restoring a single image shot captured during the exposure time. This is actually the classical case of image capturing, when the acquired image may be corrupted by motion blur, caused by the motion that have taken place during the exposure time. If the point spread function (PSF) of the motion blur is known then the original image can be restored, up to some level of accuracy (determined by the lost spatial frequencies), by applying an image restoration approach Gonzalez & Woods (1992); Jansson (1997). However, the main difficulty is that in most practical situations the motion blur PSF is not known. Moreover, since the PSF depends of the arbitrary camera motion during the exposure time, its shape is different in any degraded image as exemplified in Fig. 1. Another difficulty comes from the fact that the blur degradation is not spatially invariant over the image area. Thus, moving objects in the scene may result in very different blur models in certain image areas. On the other hand, even less dynamic scenes may contain different blur models in different regions in accordance to the distance between the objects and the camera, 1
- 20. Recent Advances inSignal Processing 2 Fig. 1. Different camera motions cause different blur degradations. i.e., during a camera translation close objects have larger relative motions than distant objects, phenomenon known as "parallax". In order to cope with the insufficient knowledge about the blur PSF one could adopt a blind de-convolution approach, e.g., Chan & Wong (1998); You & Kaveh (1996). Most of these meth- ods are computationally expensive and they have reliability problems even when dealing with spatially invariant blur. Until now, published research results have been mainly demonstrated on artificial simulations and rarely on real world images, such that their potential use in con- sumer products seems rather limited for the moment. Measurements of the camera motion during the exposure time could help in estimating the motion blur PSF and eventually to restore the original image of the scene. Such an approach have been introduced by Ben-Ezra & Nayar (2004), where the authors proposed the use of an extra camera in order to acquire motion information during the exposure time of the principal camera. A different method, based on specially designed high-speed CMOS sensors has been proposed by Liu & Gamal (2003). The method exploits the possibility to independently control the exposure time of each image pixel in a CMOS sensor. Thus, in order to prevent motion blur the integration is stopped selectively in those pixels where motion is detected. Another way to estimate the PSF has been proposed in Tico et al. (2006); Tico & Vehviläinen (2007a); Yuan et al. (2007), where a second image of the scene is taken with a short exposure. Although noisy, the secondary image is much less affected by motion blur and it can be used as a reference for estimating the motion blur PSF which degraded the principal image. In order to cope with the unknown motion blur process, designers have adopted solutions able to prevent such blur for happening in the first place. In this category are included all optical image stabilization (OIS) solutions adopted nowadays by many camera manufactures. These solutions are utilizing inertial senors (gyroscopes) in order to measure the camera mo- tion, following then to cancel the effect of this motion by moving either the image sensor Konika Minolta Inc. (2003), or some optical element Canon Inc. (2006) in the opposite direc- tion. The miniaturization of OIS systems did not reach yet the level required for implemen- tation in a small device like a camera phone. In addition, most current OIS solutions cannot cope well with longer exposure times. In part this is because the inertial motion sensors, used to measure the camera motion, are less sensitive to low frequency motions than to medium and high frequency vibrations. Also, as the exposure time increases the mechanism may drift due to accumulated errors, producing motion blurred images (Fig. 2). An image acquisition solution that can prevent motion blur consists of dividing long expo- sure times in shorter intervals, following to capture multiple short exposed image frames of
- 21. Digital Image Stabilization3 (a) (b) (c) Fig. 2. Optical image stabilization examples at different shutter speeds. The images have been captured with a hand-held camera using Canon EF-S 17-85mm image stabilized lens. The exposure times used in taking the pictures have been: (a) 1/25sec, (b) 1/8sec, and (c) 1/4sec. The images get increasingly blurred as the shutter speed slows down. the same scene. Due to their short exposure, the individual frames are corrupted by sensor noises (e.g., photon-shot noise, readout noise) Nakamura (2006) but, on the other hand, they are less affected by motion blur. Consequently, a long exposed and motion blur free picture can be synthesized by registering and fusing the available short exposed image frames (see Tico (2008a;b); Tico & Vehviläinen (2007b)). Using this technique the effect of camera motion is transformed from a motion blur degradation into a misalignment between several image frames. The advantage is that the correction of the misalignment between multiple frames is more robust and computationally less intensive than the correction of a motion blur degraded image. In this chapter we present the design of such a multi-frame image stabilization solution, ad- dressing the image registration and fusion operations. A global registration approach, de- scribed in Section 2, assists the identification of corresponding pixels between images. How- ever the global registration cannot solve for motion within the scene as well as for parallax. Consequently one can expect local misalignments even after the registration step. These will be solved in the fusion process described in Section 3. 2. Image registration Image registration is essential for ensuring an accurate information fusion between the avail- able images. The existent approaches to image registration could be classified in two cate- gories: feature based, and image based methods, Zitova & Flusser (2003). The feature based methods rely on determining the correct correspondences between different types of visual features extracted from the images. In some applications, the feature based methods are the most effective ones, as long as the images are always containing specific salient features (e.g., minutiae in fingerprint images Tico & Kuosmanen (2003)). On the other hand when the num- ber of detectable feature points is small, or the features are not reliable due to various image degradations, a more robust alternative is to adopt an image based registration approach, that
- 22. Recent Advances inSignal Processing 4 utilizes directly the intensity information in the image pixels, without searching for specific visual features. In general a parametric model for the two-dimensional mapping function that overlaps an "input" image over a "reference" image is assumed. Let us denote such mapping function by t(x; p) = [tx(x; p) ty(x; p)]t, where x = [x y]t stands for the coordinates of an image pixel, and p denotes the parameter vector of the transformation. Denoting the "input" and "refer- ence" images by h and g respectively, the objective of an image based registration approach is to estimate the parameter vector p that minimizes a cost function (e.g., the sum of square differences) between the transformed input image h(t(x; p)) and the reference image g(x). The minimization of the cost function, can be achieved in various ways. A trivial approach would be to adopt an exhaustive search among all feasible solutions by calculating the cost function at all possible values of the parameter vector. Although this method ensures the discovery of the global optimum, it is usually avoided due to its tremendous complexity. To improve the efficiency several alternatives to the exhaustive search technique have been developed by reducing the searching space at the risk of losing the global optimum, e.g., logarithmic search, three-step search, etc, (see Wang et al. (2002)). Another category of image based registration approaches, starting with the work of Lucas & Kanade (1981), and known also as gradient-based approaches, assumes that an approximation to image derivatives can be consistently estimated, such that the minimization of the cost function can be achieved by applying a gradient-descent technique (see also Baker & Matthews (2004); Thevenaz & Unser (1998)). An important efficiency improvement, for Lucas-Kanade algorithm, has been proposed in Baker & Matthews (2004), under the name of "Inverse Compositional Algorithm" (ICA). The improvement results from the fact that the Hessian matrix of the cost function, needed in the optimization process, is not calculated in each iteration, but only once in a pre- computation phase. In this work we propose an additional improvement to gradient-based methods, that consists of simplifying the repetitive image warping and interpolation operations that are required during the iterative minimization of the cost function. Our presentation starts by introducing an image descriptor in Section 2.1, that is less illumination dependent than the intensity com- ponent. Next, we present our registration algorithm in Section 2.2, that is based on matching the proposed image descriptors of the two images instead their intensity components. 2.1 Preprocessing Most of the registration methods proposed in the literature are based on matching the inten- sity components of the given images. However, there are also situations when the intensity components do not match. The most common such cases are those in which the two images have been captured under different illumination conditions, or with different exposures. In order to cope with such cases we propose a simple preprocessing step aiming to extract an illumination invariant descriptor from the intensity component of each image. Denoting by H(x) the intensity value in the pixel x, and with avg(H) the average of all intensity values in the image, we first calculate H̄(x) = H(x)/avg(H), in order to gain more independence from the global scene illumination. Next, based on the gradient of H̄ we calculate Hg(x) = ∣H̄x(x)∣ + ∣H̄y(x)∣ in each pixel, and med(Hg) as the median value of Hg(x) over the entire image.
- 23. Digital Image Stabilization5 Finally, the actual descriptor that we are using in the registration operation is given by the following binary image h(x) = { 1 if Hg(x) > med(Hg) 0 otherwise (1) 2.2 Registration algorithm In the following we describe an image based registration method that is using a multi- resolution coarse to fine strategy. Typically in such algorithm, at each iteration step one of the images should be warped in accordance to the parameters estimated so far. In our method this warping operation is highly simplified on the expense of increase memory usage. The levels of the multi-resolution representation are over-sampled, and they are obtained by iteratively smoothing the original image descriptor h, such that to obtain smoother and smoother versions of it. Let h̃ℓ denotes the smoothed image resulted after ℓ-th low-pass filter- ing iterations (h̃0 = h). The smoothed image at next iteration can be calculated by applying one-dimensional filtering along the image rows and columns as follows: h̃ℓ+1 (x, y) = ∑ r wr ∑ c wch̃ℓ ( x − 2ℓ c, y − 2ℓ r ) , (2) where wk are the taps of a low-pass filter. The registration approach takes advantage of the fact that each decomposition level (h̃ℓ) is over-sampled, and hence it can be reconstructed by a subset of its pixels. This property allows to enhance the efficiency of the registration process by using only a subset of the pixels in the registration algorithm. The advantage offered by the availability of over-sampled decompo- sition level, is that the set of pixels that can be used in the registration is not unique. A broad range of geometrical transformations can be approximated by simply choosing a different set of pixels to describe the sub-sampled image level. In this way, the over-sampled image level is regarded as a "reservoir of pixels" for different warped sub-sampled versions of the image, which are needed at different stages in the registration algorithm. Let xn,k = [xn,k yn,k]t, for n, k integers, denote the coordinates of the selected pixels into the smoothed image (h̃ℓ). A low-resolution version of the image (ĥℓ) can be obtained by col- lecting the values of the selected pixels: ĥℓ(n, k) = h̃ℓ(xn,k). Moreover, given an invertible geometrical transformation function t(x; p), the warping version of the low resolution image can be obtained more efficiently by simply selecting another set of pixels from the area of the smoothed image, rather than warping and interpolating the low-resolution image ĥℓ. This is: ĥ′ ℓ(n, k) = h̃ℓ(x′ n,k), where x′ n,k = round ( t−1(xn,k; p) ) . The process described above is illustrated in Fig.3, where the images shown on the bottom row represent two low-resolutions warped versions of the original image (shown in the top- left corner). The two low-resolution images are obtained by sampling different pixels from the smoothed image (top-right corner) without interpolation. The registration method used in our approach is presented in Algorithm 1. The algorithm follows a coarse to fine strategy, starting from a coarse resolution level and improving the pa- rameter estimate with each finer level, as details in the Algorithm 2. The proposed algorithm relies on matching image descriptors (1) derived from each image rather than image intensity components. Algorithm 2 presents the registration parameter estimation at one resolution level. In this algorithm, the constant N0, specifies the number of iterations the algorithm is performing
- 24. Recent Advances inSignal Processing 6 50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 Fig. 3. Low-resolution image warping by re-sampling an over-sampled image decomposition level. Algorithm 1 Global image registration Input: the input and reference images plus, if available, an initial guess of the parameter vector p = [p1 p2 ⋅ ⋅ ⋅ pK]t. Output: the parameter vector that overlaps the input image over the reference image. 1- Calculate the descriptors (1) for input and reference images, denoted here by h and g, respectively. 2- Calculate the decomposition levels of the two image descriptors {h̃ℓ, g̃ℓ ∣ ℓmin ≤ ℓ ≤ ℓmax}. 3- For each level ℓ between ℓmax and ℓmin, do Algorithm 2. after finding a minima of the error function. This is set in order to reduce the chance of ending in a local minima. As shown in the algorithm the number of iterations is reset to N0, every time a new minima of the error function is found. The algorithm stops only if no other minima is found in N0 iterations. In our experiments a value N0 = 10 has been used.
- 25. Digital Image Stabilization7 Algorithm 2 Image registration at one level Input: the ℓ-th decomposition level of the input and reference images (h̃ℓ, g̃ℓ), plus the parameter vector p = [p1 p2 ⋅ ⋅ ⋅ pK]t estimated at the previous coarser level. Output: a new estimate of the parameter vector pout that overlaps h̃ℓ over g̃ℓ. Initialization: set minimum matching error Emin = ∞, number of iterations Niter = N0 1- Set the initial position of the sampling points xn,k in the vertex of a rectangular lattice of period D = 2ℓ, over the area of the reference image g̃ℓ. 2- Construct the reference image at this level: ĝ(n, k) = g̃ℓ(xn,k). 3- For each parameter pi of the warping function calculate the image Ji(n, k) = ĝx(n, k) ∂tx(x; 0) ∂pi + ĝy(n, k) ∂ty(x; 0) ∂pi where ĝx, ĝy denote a discrete approximation of the gradient components of the reference image. 4- Calculate the first order approximation of the K × K Hessian matrix, whose element (i, j) is given by: H(i, j) = ∑ n,k Ji(n, k)Jj(n, k) 5- Calculate a K × K updating matrix U, as explain in the text. Iterations: while Niter > 0 6- Construct the warped low-resolution input image in accordance to the warping param- eters estimated so far: ĥ(n, k) = h̃ℓ(round ( t−1(xn,k; p) ) ). 7- Determine the overlapping area between ĥ and ĝ, as the set of pixel indices Ψ such that any pixel position (n, k) ∈ Ψ is located inside the two images. 8- Calculate the error image e(n, k) = ĥ(n, k) − ĝ(n, k), for any (n, k) ∈ Ψ. 9- Calculate a smooth version ẽ of the error image by applying a 2 × 2 constant box filter, and determine total error E = ∑(n,k)∈Ψ ∣ẽ(n, k)∣. 10- If E ≥ Emin then Niter = Niter − 1, otherwise update Emin = E, Niter = N0, and pout = p. 11- Calculate the K × 1 vector q, with q(i) = ∑(n,k)∈Ψ ẽ(n, k)Ji(n, k). 12- Update the parameter vector p = p + Uq The parameter update (i.e., line 12 in Algorithm 2) makes use of an updating matrix U calcu- lated in step 5 of the algorithm. This matrix depends of the functional form of the geometrical transformation assumed between the two images, t(x; p). For instance, in case of affine trans-
- 26. Recent Advances inSignal Processing 8 formation t(x; p) = [ (1 − p3)x + p4y + p1 p5x + (1 − p6)y + p2 ] , (3) the parameter update matrix is U = diag (D, D, 1, 1, 1, 1) H−1 , (4) whereas in case of a projective transformation t(x; p) = [ (1 − p3)x + p4y + p1 p5x + (1 − p6)y + p2 ] /(p7x + p8y + 1), (5) we have U = diag (D, D, 1, 1, 1, 1, 1/D, 1/D) H−1 . (6) In our implementation of multi-resolution image decomposition (2), we used a symmetric filter w of size 3, whose taps are respectively w−1 = 1/4, w0 = 1/2, and w1 = 1/4. Also, in order to reduce the storage space the first level of image decomposition (i.e., h̃1), is sub- sampled by 2, such that any higher decomposition level is half the size of the original image. 3. Fusion of multiple images The pixel brightness delivered by an imaging system is related to the exposure time through a non-linear mapping called "radiometric response function", or "camera response function" (CRF). There are a variety of techniques (e.g., Debevec & Malik (1997); Mitsunaga & Nayar (1999)) that can be used for CRF estimation. In our work we assume that the CRF function of the imaging system is known, and based on that we can write down the following relation for the pixel brightness value: I(x) = CRF (g(x)∆t) (7) where x = [x y]T denotes the spatial position of an image pixel, I(x) is the brightness value delivered by the system, g(x) denotes the irradiance level caused by the light incident on the pixel x of the imaging sensor, and ∆t stands for the exposure time of the image. Let Ik, for k ∈ {1, . . . , K} denote the K observed image frames whose exposure times are denoted by ∆tk. A first step in our algorithm is to convert each image to the linear (irradiance) domain based on knowledge about the CRF function, i.e., gk(x) = (1/∆tk) CRF−1 (Ik(x)) , for all k ∈ {1, . . . , K}. (8) We assume the following model for the K observed irradiance images: gk(x) = fk(x) + nk(x), (9) where where x = [x y]T denotes the spatial position of an image pixel, gk is the k-th observed image frame, nk denotes a zero mean additive noise, and fk denotes the latent image of the scene at the moment the k-th input frame was captured. We emphasize the fact that the scene may change between the moments when different input frames are captured. Such changes could be caused by unwanted motion of the camera and/or by the motion of different objects in the scene. Consequently, the algorithm can provide a number of K different estimates of the latent scene image each of them corresponding to a different reference moment.
- 27. Digital Image Stabilization9 In order to preserve the consistency of the scene, we select one of the input images as reference, following to aim for improving the selected image based on the visual data available in all captured images. In the following, we denote by gr, (r ∈ {1, . . . , K}) the reference image observation, and hence the objective of the algorithm is to recover an estimate of the latent scene image at moment r, i.e., f = fr. The restoration process is carried out based on a spatiotemporal block processing. Assuming a division of gr in non-overlapping blocks of size B × B pixels, the restored version of each block is obtained as a weighted average of all blocks located in a specific search range, inside all observed images. Let XB x denote the sub-set of spatial locations included into a block of B × B pixels centered in the pixel x, i.e.: XB x = { y ∈ Ω ∣ [−B − B]T < 2 (y − x) ≤ [B B]T } , (10) where the inequalities are componentwise, and Ω stands for the image support. Also, let g(XB x ) denote the B2 × 1 column vector comprising the values of all pixels from an image g that are located inside the block XB x . The restored image is calculated block by block as follows ˆ f (XB x ) = 1 Z K ∑ k=1 ∑ y∈XS x wk (x, y) gk(XB y ), for all XB x , (11) where Z = ∑K k=1 ∑y∈XS x wk (x, y), is a normalization value, XS x denotes the spatial search range of size S × S centered in x, and wk (x, y) is a scalar weight value assigned to an input block XB y from image gk. The weight values are emphasizing the input blocks that are more similar with the reference block. Note that, at the limit, by considering only the most similar such block from each input image we obtain the block corresponding to the optical flow between the reference image and that input image, as in Tico & Vehviläinen (2007b). In such a case the weighted average (11) comprises only a small number of contributing blocks for each reference block. If more com- putational power is available, we can chose the weight values such that to use more blocks for the restoration of each reference block, like for instance in the solution presented in Tico (2008a), where the restoration of each reference block is carried out by considering all visu- ally similar blocks found either inside the reference image or inside any other input image. Although the use of block processing is more efficient for large images, it might create arti- facts in detailed image areas. In order to cope with this aspect, the solution presented in Tico (2008a), proposes a mechanism for adapting the block size to the local image content, by us- ing smaller blocks in detail areas and larger blocks in smooth areas of the image. We conclude this section by summarizing the operations of a multi-frame image stabilization solutions in Algorithm 3.
- 28. Recent Advances inSignal Processing 10 Algorithm 3 Stabilization algorithm Input: multiple input images of the scene. Output: one stabilized image of the scene. 1- Select a reference image either in a manual or an automatic manner. Manual selection can be based on preferred scene content at the moment the image frame was captured, whereas automatic selection could be trivial (i.e., selecting the first frame), or image quality based (i.e., selecting the higher quality frame based on a quality criteria). In our work we select the reference image frame as the one that is the least affected by blur. To do this we employ a sharpness measure, that consists of the average energy of the image in the middle frequency band, calculated in the FFT domain. 2- Convert the input images to a linear color space by compensating for camera response function non-linearity. 3- Register the input images with respect to the reference image. 4- Estimate the additive noise variance in each input image. Instead using a global vari- ance value for the entire image, in our experiments we employed a linear model for the noise variance with respect to the intensity level in order to emulate the Poisson process of photon counting in each sensor pixel. 5- Restore each block of the reference image in accordance to (11). 6- Convert the resulted irradiance estimate ˆ f (x), of the final image, back to the image domain, Î(x) = CRF( ˆ f (x)∆t), based on the desired exposure time ∆t. Alternatively, in order to avoid saturation and hence to extend the dynamic range of the captured image, one can employ a tone mapping procedure (e.g., Jiang & Guoping (2004)) for converting the levels of the irradiance image estimate into the limited dynamic range of the display system.
- 29. Digital Image Stabilization11 (a) (b) (c) (d) Fig. 4. Real image example: (a) one input image out of four, (b) overlapping all four input images, (c,d) two different results obtained by selecting different reference moments. (a) (b) Fig. 5. Fragment from Fig. 4: (a) the digitally gained reference image, (b) the same fragment from the result.
- 30. Recent Advances inSignal Processing 12 (a) (b) Fig. 6. Real imaging examples: (a) auto-exposed image taken with a camera phone (exposure time: 1.8 sec), (b) stabilized image by fusing four frames with exposure time of 0.3 sec each. (a) (b) Fig. 7. Applying the proposed algorithm onto a single input image (a), delivers a noise filtered version (b), of the input image. 4. Examples A visual example of the presented method is shown in Fig. 4. In total a number of four short exposed image frames (like the one shown in Fig. 4(a)) have been captured. During the time the individual images have been captured the scene was changed due to moving objects, as reveal by Fig. 4 (b). Applying the proposed algorithm we can recover a high quality image at any moment by choosing the reference frame properly, as exemplified by Fig. 4 (c) and (d). The improvement in image quality achieved by combining multiple images is demonstrated by the fragment in Fig. 5 that shows significant reduction in image noise between one input image Fig. 5(a) and the result Fig. 5(b). Two examples using images captured with a mobile phone camera are shown in Fig. 6 and Fig. 7. In both cases the algorithm was applied onto the Bayer RAW image data before image
- 31. Digital Image Stabilization13 pipeline operations. A simple linear model for the noise variance with respect to the intensity level was assumed in order to emulate the Poisson process of photon counting in each sensor pixel Nakamura (2006), for each color channel. Fig. 6(a), shows an image obtained without stabilization using the mobile device set on au- tomatic exposure. Due to unwanted camera motion the resulted image is rather blurry. For comparison, Fig. 6(b), shows the image obtained with our proposed stabilization algorithm by fusing several short exposed images of the same scene. An example when the proposed algorithm is applied onto a single input image is shown in Fig. 7. In this case the algorithm acts as a noise filtering method delivering the image Fig. 7(b), by reducing the noise present in the input image Fig. 7(a). 5. Conclusions and future work In this chapter we presented a software solution to image stabilization based on fusing the visual information between multiple frames of the same scene. The main components of the algorithm, global image registration and image fusion have been presented in detail along with several visual examples. An efficient coarse to fine image based registration solution is obtained by preserving an over-sampled version of each pyramid level in order to simplify the warping operation in each iteration step. Next the image fusion step matches the visual similar image blocks between the available frames coping thereby with the presence of mov- ing objects in the scene or with the inability of the global registration model to describe the camera motion. The advantages of such a software solution against the popular hardware opto-mechanical image stabilization systems include: (i) the ability to prevent blur caused by moving objects in a dynamic scene, (ii) the ability to deal with longer exposure times and stabilized not only high frequency vibrations but also low frequency camera motion during the integration time, and (iii) the reduced cost and size required for implementation in small mobile devices. The main disadvantage is the need to capture multiple images of the scene. However, nowadays most camera devices provide a "burst" mode that ensures fast capturing of multiple images. Future work would have to address several other applications that can take advantage of the camera "burst" mode by fusing multiple images captured with similar of different exposure and focus parameters. 6. References Baker, S. & Matthews, I. (2004). Lucas-Kanade 20 Years On: A Unifying Framework, Interna- tional Journal of Computer Vision . Ben-Ezra, M. & Nayar, S. K. (2004). Motion-Based Motion Deblurring, IEEE Transactions on Pattern Analysis and Machine Intelligence 26(6): 689–698. Canon Inc. (2006). Shift-Method Optical Image Stabilizer. URL: www.canon.com/technology/dv/02.html Chan, T. F. & Wong, C.-K. (1998). Total Variation Blind Deconvolution, IEEE Transactions on Image Processing 7(3): 370–375. Debevec, P. E. & Malik, J. (1997). Recovering High Dynamic Range Radiance Maps from Pho- tographs, Proc. of International Conference on Computer Graphics and Interactive Tech- niques (SIGGRAPH). Erturk, S. & Dennis, T. (2000). Image sequence stabilization based on DFT filtering, IEE Proc. On Vision Image and Signal Processing 147(2): 95–102. Gonzalez, R. C. & Woods, R. E. (1992). Digital Image Processing, Addison-Wesley.
- 32. Recent Advances inSignal Processing 14 Jansson, P. (1997). Deconvolution of image and spectra, Academic Press. Jiang, D. & Guoping, Q. (2004). Fast tone mapping for high dynamic range images, Proc. of 17th Intl. Conf. on Pattern Recognition (ICPR), Vol. 2, pp. 847–850. Konika Minolta Inc. (2003). Anti-Shake Technology, www.konicaminolta.com/ prod- ucts/consumer/digital camera/dimage/dimage-a2/02.html . Liu, X. & Gamal, A. E. (2003). Synthesis of high dynamic range motion blur free image from multiple captures, IEEE Transaction on Circuits and Systems-I 50(4): 530–539. Lucas, B. D. & Kanade, T. (1981). An Iterative Image Registration Technique with an Appli- cation to Stereo Vision, Proc. of 7th Intl Conf on Artificial Intelligence (IJCAI), Vancou- ver,Canada, pp. 674–679. Mitsunaga, T. & Nayar, S. K. (1999). Radiometric self calibration, Proc. of Conference on Com- puter Vision and Pattern Recognition. Nakamura, J. (2006). Basics of image sensors, in J. Nakamura (ed.), Image Sensors and Signal Processing for Digital Still Cameras, CRC Press, pp. 53–94. Thevenaz, P. & Unser, M. (1998). A Pyramid Approach to Subpixel Registration Based on Intensity, IEEE Transactions on Image Processing 7(1): 27–41. Tico, M. (2008a). Adaptive block-based approach to image stabilization, Proc. of the IEEE Inter- national Conference of Image Processing (ICIP), Vol. 1, San Diego, CA, USA, pp. 521–524. Tico, M. (2008b). Multiframe image denoising and stabilization, Proc. of the 15th European Signal Processing Conference (EUSIPCO), Lausanne, Switzerland. Tico, M. & Kuosmanen, P. (2003). Fingerprint matching using an orientation-based minutia descriptor, IEEE Trans. on Pattern Analysis and Machine Intelligence 25(8): 1009–1014. Tico, M., Trimeche, M. & Vehviläinen, M. (2006). Motion blur identification based on dif- ferently exposed images, Proc. of the IEEE International Conference of Image Processing (ICIP), Atlanta, GA, USA, pp. 2021–2024. Tico, M. & Vehviläinen, M. (2005). Constraint motion filtering for video stabilization, Proc. of the IEEE International Conference of Image Processing (ICIP), Vol. 3, Genova, Italy, pp. 569–572. Tico, M. & Vehviläinen, M. (2007a). Image stabilization based on fusing the visual informa- tion in differently exposed images, Proc. of the IEEE International Conference of Image Processing (ICIP), Vol. 1, San Antonio, TX, USA, pp. 117–120. Tico, M. & Vehviläinen, M. (2007b). Robust image fusion for image stabilization, IEEE In- ternational Conference on Acoustics, Speech, and Signal Processing (ICASSP), Honolulu, USA. Wang, Y., Ostermann, J. & Zhang, Y.-Q. (2002). Video Processing and Communications, Prentice Hall. You, Y.-L. & Kaveh, M. (1996). A regularization approach to joint blur identification and image restoration, IEEE Trans. on Image Processing 5(3): 416–428. Yuan, L., Sun, J., Quan, L. & Shum, H.-Y. (2007). Image deblurring with blurred/noisy image pairs, ACM Transactions on Graphics 26(3). Zitova, B. & Flusser, J. (2003). Image registration methods: a survey, Image and Vision Comput- ing 21: 977–1000.
- 33. About array processingmethods for image segmentation 15 X About array processing methods for image segmentation J. Marot, C. Fossati Institut Fresnel (Ecole Centrale Marseille) France Y. Caulier Fraunhofer Institute IIS Germany 1. Introduction Shape description is an important goal of computational vision and image processing. Giving the characteristics of lines or distorted contours is faced in robotic way screening, measuring of wafer track width in microelectronics, aerial image analysis, vehicle trajectory and particle detection. Distorted contour retrieval is also encountered in medical imaging. In this introduction, we firstly present classical methods that were proposed to solve this problem, that is, Snakes and levelset methods (Kass et al., 1988; Xu & Prince, 1997; Zhu & Yuile, 1996; Osher & Sethian, 1988; Paragios & Deriche, 2002). We secondly present original methods which rely on signal generation out of an image and adaptation of high resolution methods of array processing (Aghajan & Kailath, 1993a; Aghajan, 1995; Bourennane & Marot, 2006; Marot & Bourennane, 2007a; Marot & Bourennane, 2007b; Marot & Bourennane, 2008). A Snake is a closed curve which, starting from an initial position, evolves towards an object of interest under the influence of forces (Kass et al., 1988; Xu & Prince, 1997; Zhu & Yuile, 1996; Xianhua & Mirmehdi, 2004; Cheng & Foo 2006; Brigger et al., 2000) Snakes methods are edge-based segmentation schemes which aim at finding out the transitions between uniform areas, rather than directly identifying them (Kass et al., 1988; Xu & Prince, 1997). Another model of active contour is geodesic curves or "levelset". Its main interest with respect to Snakes is to be able to face changes in topology, to the cost of a higher computational load (Osher & Sethian, 1988; Paragios & Deriche 2002; Karoui et al., 2006). We describe here more precisely Snakes type methods because they are edge-based methods as well as the proposed array processing methods. Edge-based segmentation schemes have improved, considering robustness to noise and sensitivity to initialization (Xu & Prince, 1997). Some active contour methods were combined with spline type interpolation to reduce the number of control points in the image (Brigger et al. 2000). This increases the robustness to noise and computational load. In particular, (Precioso et al., 2005) uses smoothing splines in the B-spline interpolation approach of (Unser et al. 1993). In (Xu & Prince, 1997) the proposed "Gradient Vector Flow" (GVF) method provides valuable results, but is prone to 2
- 34. Recent Advances inSignal Processing 16 shortcomings: contours with high curvature may be skipped unless an elevated computational load is devoted. Concerning straight lines in particular, in (Kiryati & Brucktein, 1992; Sheinval & Kiryati, 1997) the extension of the Hough transform retrieves the main direction of roughly aligned points. This method gives a good resolution even with noisy images. Its computational load is elevated. Least-squares fit of straight lines seeks to minimize the summation of the squared error-of-fit with respect to measures (Gander et al., 1994; Connel & Jain, 2001). This method is sensitive to outliers. An original approach in contour estimation consists in adapting high-resolution methods of array processing (Roy & Kailath, 1989; Pillai & Kwon, 1989; Marot et al., 2008) for straight line segmentation (Aghajan & Kailath, 1993a; Aghajan, 1995; Aghajan & Kailath, 1993b; Halder et al., 1995; Aghajan & Kailath, 1994; Aghajan & Kailath, 1992). In this framework, a straight line in an image is considered as a wave-front. Now, high-resolution methods of array processing have improved for several years (Roy & Kailath, 1989; Bourennane et al., 2008). In particular, sensitivity to noise has improved, and the case of correlated sources is faced by a "spatial smoothing" procedure (Pillai & Kwon 1989). To adapt high-resolution methods of array processing to contour estimation in images, the image content is transcripted into a signal through a specific generation scheme, performed on a virtual set of sensors located along the image side. In (Abed-Meraim & Hua, 1997), a polynomial phase model for the generated signal is proposed to take into account the image discretization, for an improved straight line characterization. The ability of high-resolution methods to handle correlated sources permitted to handle the case of parallel straight lines in image understanding (Bourennane & Marot, 2006; Bourennane & Marot, 2005). Optimization methods generalized straight line estimation to nearly straight distorted contour estimation (Bourennane & Marot, 2005; Bourennane & Marot, 2006b; Bourennane & Marot, 2006c). Circular and nearly circular contour segmentation (Marot & Bourennane, 2007a; Marot & Bourennane, 2007b) was also considered. While straight and nearly straight contours are estimated through signal generation on linear antenna, circular and nearly circular contour segmentation is performed through signal generation upon circular antenna. We adapt the shape of the antenna to the shape of the expected contours so we are able to apply the same high-resolution and optimization methods as for straight and nearly straight line retrieval. In particular array processing methods for star-shaped contour estimation provide a solution to the limitation of Snakes active contours concerning contours with high concavity (Marot & Bourennane, 2007b). The proposed multiple circle estimation method retrieves intersecting circles, thus providing a solution to levelset-type methods. The remainder of the chapter is organized as follows: We remind in section 2 the formalism that adapts the estimation of straight lines as a classical array processing problem. The study dedicated to straight line retrieval is used as a basis for distorted contour estimation (see section 3). In section 4 we set the problem of star-shaped contour retrieval and propose a circular antenna to retrieve possibly distorted concentric circles. In section 5 we summarize the array processing methods dedicated to possibly distorted linear and circular contour estimation. We emphasize the similarity between nearly linear and nearly circular contour estimation. In section 6 we show how signal generation on linear antenna yields the coordinates of the center of circles. In section 7 we describe a method for the estimation of intersecting circles, thereby proposing a solution to a limitation of the levelset type algorithms. In section 8 we propose some results through various applications: robotic vision, omni directional images, and medical melanoma images.
- 35. About array processingmethods for image segmentation 17 2. Straight contour estimation 2.1 Data model, generation of the signals out of the image data To adapt array processing techniques to distorted curve retrieval, the image content must be transcripted into a signal. This transcription is enabled by adequate conventions for the representation of the image, and by a signal generation scheme (Aghajan, 1995; Aghajan & Kailath, 1994). Once a signal has been created, array processing methods can be used to retrieve the characteristics of any straight line. Let I be the recorded image (see Fig.1 (a).). Fig. 1. The image model (see Aghajan & Kailath, 1992): (a) The image-matrix provided with the coordinate system and the linear array of N equidistant sensors, (b) A straight line characterized by its angle and its offset 0 x . We consider that I contains d straight lines and an additive uniformly distributed noise. The image-matrix is the discrete version of the recorded image, compound of a set of N C pixel values. A formalism adopted in (Aghajan & Kailath, 1993) allows signal generation, by the following computation: C k ,.......,N i jµk), ( exp I(i,k) z(i) 1 1 (1) Where C ,..., k ; N ,..., i ); k , i ( I 1 1 denote the image pixels. Eq. (1) simulates a linear antenna: each row of the image yields one signal component as if it were associated with a sensor. The set of sensors corresponding to all rows forms a linear antenna. We focus in the following on the case where a binary image is considered. The contours are composed of 1- valued pixels also called "edge pixels", whereas 0-valued pixels compose the background. When d straight lines, with parameters angle k and offset ) d ,..., k ( x k 1 0 , are crossing the image, and if the image contains noisy outlier pixels, the signal generated on the ith sensor, in front of the ith row, is (Aghajan & Kailath, 1993): d k k k i n jµx exp ) tan i (jµ exp z(i) 1 0 1 (2)
- 36. Recent Advances inSignal Processing 18 Where µ is a propagation parameter (Aghajan & Kailath, 1993b) and n(i) is due to the noisy pixels on the ith row. Defining k k k k i jµx exp s , tan i jµ exp a 0 1 , Eq. (2) becomes: N ,..., i , i n s a z(i) d k k k i 1 1 (3) Grouping all terms in a single vector, Eq. (3) becomes: n s A z θ , with d 1 θ ,..., θ θ a a A where T k N k k k a ,..., a , a 2 1 a , with N ,..., i , tan i jµ exp a k k i 1 1 , superscript T denoting transpose. SLIDE (Subspace- based Line DEtection) algorithm (Aghajan & Kailath, 1993) uses TLS-ESPRIT (Total-Least- Squares Estimation of Signal Parameters via Rotational Invariance Techniques) method to estimate the angle values. To estimate the offset values, the "extension of the Hough transform" (Kiryati & Bruckstein, 1992) can be used. It is limited by its high computational cost and the large required size for the memory bin. (Bourennane & Marot, 2006a; Bourennane & Marot, 2005) developed another method. This method remains in the frame of array processing and reduces the computational cost: A high-resolution method called MFBLP (Modified Forward Backward Linear Prediction) (Bourennane & Marot, 2005) is associated with a specific signal generation method, namely the variable parameter propagation scheme (Aghajan & Kailath, 1993b). The formalism introduced in that section can also handle the case of straight edge detection in gray-scale images (Aghajan & Kailath, 1994). In the next section, we consider the estimation of the straight line angles and offsets, by reviewing the SLIDE and MFBLP methods. 2.2 Angle estimation, overview of the SLIDE method The method for angles estimation falls into two parts: the estimation of a covariance matrix and the application of a total least squares criterion. Numerous works have been developed in the frame of the research of a reliable estimator of the covariance matrix when the duration of the signal is very short or the number of realizations is small. This situation is often encountered, for instance, with seismic signals. To cope with it, numerous frequency and/or spatial means are computed to replace the temporal mean. In this study the covariance matrix is estimated by using the spatial mean (Halder & al., 1995). From the observation vector we build K vectors of length M with 1 d N M d . In order to maximize the number of sub-vectors we choose K=N+1- M. By grouping the whole sub-vectors obtained in matrix form, we obtain : K K ,...,z z Z 1 , where K ,..., l , s l l M l 1 n A z . Matrix d 1 θ ,..., θ θ a a AM is a Vandermonde type one of size M x d. Signal part of the data is supposed to be independent from the noise; the components of noise vector l n are supposed to be uncorrelated, and to have identical variance. The covariance matrix can be estimated from the observation sub-vectors as it is performed in (Aghajan & Kailath, 1992). The eigen-decomposition of the covariance matrix is, in general, used to characterize the sources by subspace techniques in array processing. In the frame of image processing the aim is to estimate the angle of the d straight lines. Several high-resolution methods that solve this problem have been proposed (Roy & Kailath, 1989). SLIDE algorithm is applied to a particular case of an array consisting of two
- 37. About array processingmethods for image segmentation 19 identical sub-arrays (Aghajan & Kailath, 1994). It leads to the following estimated angles (Aghajan & Kailath, 1994): k k k ln Im * µ tan ˆ 1 1 (4) where d ,..., k , k 1 are the eigenvalues of a diagonal unitary matrix that relates the measurements from the first sub-array to the measurements resulting from the second sub- array. Parameter is the propagation constant, and Δ is the distance between two sensors. TLS-ESPRIT method used by SLIDE provides the estimated parameters in closed-form, in opposite to the Hough transform which relies on maxima research (Kiryati & Bruckstein, 1992). Offset estimation exploits the estimated straight lines angles. 2.3 Offset estimation The most well-known offset estimation method is the "Extension of the Hough Transform" (Sheinvald & Kiryati, 1997). Its principle is to count all pixel aligned on several orientations. The expected offset values correspond to the maximum pixel number, for each orientation value. The second proposed method remains in the frame of array processing: it employs a variable parameter propagation scheme (Aghajan, 1993; Aghajan & Kailath, 1993b; Aghajan & Kailath, 1994) and uses a high resolution method. This high resolution "MFBLP" method relies on the concept of forward and backward organization of the data (Pillai & Kwon, 1989; Halder, Aghajan et al., 1995; Tufts & Kumaresan, 1982). A variable speed propagation scheme (Aghajan & Kailath, 1993b; Aghajan & Kailath, 1994), associated with "MFBLP" (Modified Forward Backward Linear Prediction) yields offset values with a lower computational load than the Extension of the Hough Transform. The basic idea in this method is to associate a propagation speed which is different for each line in the image (Aghajan & Kailath, 1994). By setting artificially a propagation speed that linearly depends on row indices, we get a linear phase signal. When the first orientation value is considered, the signal received on sensor ) N ,... i ( i 1 is then: 1 1 1 0 1 d k k i n tan i j exp ) x j ( exp z(i) (5) 1 d is the number of lines with angle 1 . When varies linearly as a function of the line index the measure vector z contains a modulated frequency term. Indeed we set 1 i . 1 1 1 2 0 1 1 d k k i n tan i j exp ) x i j ( exp z(i) (6) This is a sum of 1 d signals that have a common quadratic phase term but different linear phase terms. The first treatment consists in obtaining an expression containing only linear terms. This goal is reached by dividing z(i) by the non zero term 1 2 1 1 tan i j exp ) ( ai . We obtain then:
- 38. Recent Advances inSignal Processing 20 1 1 0 1 d k k i ' n x i j exp i w (7) The resulting signal appears as a combination of 1 d sinusoids with frequencies: 1 0 1 2 d ,..., k , x f k k (8) Consequently, the estimation of the offsets can be transposed to a frequency estimation problem. Estimation of frequencies from sources having the same amplitude was considered in (Tufts & Kumaressan, 1982). In the following a high resolution algorithm, initially introduced in spectral analysis, is proposed for the estimation of the offsets. After adopting our signal model we adapt to it the spectral analysis method called modified forward backward linear prediction (MFBLP) (Tufts & Kumaresan, 1982) for estimating the offsets: we consider k d straight lines with given angle k , and apply the MFBLP method, to the vector w . Details about MFBLP method applied to offset estimation are available in (Bourennane & Marot, 2006a). MFBLP estimates the values of 1 1 d ,..., k , fk . According to Eq. (8) these frequency values are proportional to the offset values, the proportionality coefficient being . The main advantage of this method comes from its low computational load. Indeed the complexity of the variable parameter propagation scheme associated with MFBLP is much less than the complexity of the Extension of the Hough Transform as soon as the number of non zero pixels in the image increases. This algorithm enables the characterization of straight lines with same angle and different offset. 3. Nearly linear contour retrieval In this section, we keep the same signal generation formalism as for straight line retrieval. The more general case of distorted contour estimation is proposed. The reviewed method relies on constant speed signal generation scheme, and on an optimization method. 3.1 Initialization of the proposed algorithm To initialize our recursive algorithm, we apply SLIDE algorithm, which provides the parameters of the straight line that fits the best the expected distorted contour. In this section, we consider only the case where the number d of contours is equal to one. The parameters angle and offset recovered by the straight line retrieval method are employed to build an initialization vector 0 x , containing the initialization straight line pixel positions: T tan N x ,..., tan x , x 1 0 0 0 0 x Fig.2 presents a distorted curve, and an initialization straight line that fits this distorted curve.
- 39. About array processingmethods for image segmentation 21 Fig. 2. A model for an image containing a distorted curve 3.2 Distorted curve: proposed algorithm We aim at determining the N unknowns N ,..., i , i x 1 of the image, forming a vector input x , each of them taken into account respectively at the th i sensor: N ,..., i , i jµx exp i z 1 (9) The observation vector is T N jµx exp ,..., jµx exp 1 input z (1 0) We start from the initialization vector 0 x , characterizing a straight line that fits a locally rectilinear portion of the expected contour. The values N ,..., i , i x 1 can be expressed as: N ,..., i , i x tan i x i x 1 1 0 where i x is the pixel shift for row i between a straight line with parameters and the expected contour. Then, with k indexing the steps of this recursive algorithm, we aim at minimizing 2 x for estimated input k k z z x J (11) where . represents the N C norm. For this purpose we use fixed step gradient method: N k : k k 1 k x x x J , is the step for the descent. At this point, by minimizing criterion J (see Eq. (11)), we find the components of vector x leading to the signal z which is the closest to the input signal in the sense of criterion J . Choosing a value of µ which is small enough (see Eq. (1)) avoids any phase indetermination. A variant of the fixed step gradient method is the variable step gradient method. It consists in adopting a descent step which depends on the iteration index. Its purpose is to accelerate the convergence of gradient. A more elaborated optimization method based on DIRECT algorithm (Jones et al., 1993) and spline interpolation (Marot & Bourennane, 2007a) can be adopted to reach the global minimum of criterion J of Eq. (11). This method is applied to modify recursively signal k x for estimated z : at each step of the recursive procedure vector k x is computed by making an interpolation between some "node" values that are retrieved by DIRECT. The
- 40. Recent Advances inSignal Processing 22 interest of the combination of DIRECT with spline interpolation comes from the elevated computational load of DIRECT. Details about DIRECT algorithm are available in (Jones et al., 1993). Reducing the number of unknown values retrieved by DIRECT reduces drastically its computational load. Moreover, in the considered application, spline interpolation between these node values provides a continuous contour. This prevents the pixels of the result contour from converging towards noisy pixels. The more interpolation nodes, the more precise the estimation, but the slower the algorithm. After considering linear and nearly linear contours, we focus on circular and nearly circular contours. 4. Star-shape contour retrieval Star-shape contours are those whose radial coordinates in polar coordinate system are described by a function of angle values in this coordinate system. The simplest star-shape contour is a circle, centred on the origin of the polar coordinate system. Signal generation upon a linear antenna yields a linear phase signal when a straight line is present in the image. While expecting circular contours, we associate a circular antenna with the processed image. By adapting the antenna shape to the shape of the expected contour, we aim at generating linear phase signals. 4.1 Problem setting and virtual signal generation Our purpose is to estimate the radius of a circle, and the distortions between a closed contour and a circle that fits this contour. We propose to employ a circular antenna that permits a particular signal generation and yields a linear phase signal out of an image containing a quarter of circle. In this section, center coordinates are supposed to be known, we focus on radius estimation, center coordinate estimation is explained further. Fig. 3(a) presents a binary digital image I . The object is close to a circle with radius value r and center coordinates c c m , l . Fig. 3(b) shows a sub-image extracted from the original image, such that its top left corner is the center of the circle. We associate this sub-image with a set of polar coordinates , , such that each pixel of the expected contour in the sub-image is characterized by the coordinates , r , where is the shift between the pixel of the contour and the pixel of the circle that roughly approximates the contour and which has same coordinate . We seek for star-shaped contours, that is, contours that can be described by the relation: f where f is any function that maps 2 0, to R . The point with coordinate 0 corresponds then to the center of gravity of the contour. Generalized Hough transform estimates the radius of concentric circles when their center is known. Its basic principle is to count the number of pixels that are located on a circle for all possible radius values. The estimated radius values correspond to the maximum number of pixels.
- 41. About array processingmethods for image segmentation 23 Fig. 3. (a) Circular-like contour, (b) Bottom right quarter of the contour and pixel coordinates in the polar system , having its origin on the center of the circle. r is the radius of the circle. is the value of the shift between a pixel of the contour and the pixel of the circle having same coordinate Contours which are approximately circular are supposed to be made of more than one pixel per row for some of the rows and more than one pixel per column for some columns. Therefore, we propose to associate a circular antenna with the image which leads to linear phase signals, when a circle is expected. The basic idea is to obtain a linear phase signal from an image containing a quarter of circle. To achieve this, we use a circular antenna. The phase of the signals which are virtually generated on the antenna is constant or varies linearly as a function of the sensor index. A quarter of circle with radius r and a circular antenna are represented on Fig.4. The antenna is a quarter of circle centered on the top left corner, and crossing the bottom right corner of the sub-image. Such an antenna is adapted to the sub-images containing each quarter of the expected contour (see Fig.4). In practice, the extracted sub-image is possibly rotated so that its top left corner is the estimated center. The antenna has radius R so that s N R 2 where s N is the number of rows or columns in the sub-image. When we consider the sub-image which includes the right bottom part of the expected contour, the following relation holds: c c s m N , l N max N where c l and c m are the vertical and horizontal coordinates of the center of the expected contour in a cartesian set centered on the top left corner of the whole processed image (see Fig.3). Coordinates c l and c m are estimated by the method proposed in (Aghajan, 1995), or the one that is detailed later in this paper. Signal generation scheme upon a circular antenna is the following: the directions adopted for signal generation are from the top left corner of the sub-image to the corresponding sensor. The antenna is composed of S sensors, so there are S signal components.
- 42. Recent Advances inSignal Processing 24 Fig. 4. Sub-image, associated with a circular array composed of S sensors Let us consider i D , the line that makes an angle i with the vertical axis and crosses the top left corner of the sub-image. The th i component S ,..., i 1 of the z generated out of the image reads: s i N m , l D m , l m , l m l j exp m , l I i z 1 2 2 (12) The integer l (resp. m ) indexes the lines (resp. the columns) of the image. j stands for 1 . µ is the propagation parameter (Aghajan & Kailath, 1994). Each sensor indexed by i is associated with a line i D having an orientation S i i 2 1 . In Eq. (2), the term m , l means that only the image pixels that belong to i D are considered for the generation of the th i signal component. Satisfying the constraint i D m , l , that is, choosing the pixels that belong to the line with orientation i , is done in two steps: let setl be the set of indexes along the vertical axis, and setm the set of indexes along the horizontal axis. If i is less than or equal to 4 , s N : setl 1 and i s tan . N : setm 1 . If i is greater than 4 , s N : setm 1 and i s tan . N : setl 2 1 . Symbol . means integer part. The minimum number of sensors that permits a perfect characterization of any possibly distorted contour is the number of pixels that would be virtually aligned on a circle quarter having radius s N 2 . Therefore, the minimum number S of sensors is s N 2 . 4.2 Proposed method for radius and distortion estimation In the most general case there exists more than one circle for one center. We show how several possibly close radius values can be estimated with a high-resolution method. For this, we use a variable speed propagation scheme toward circular antenna. We propose a method for the estimation of the number d of concentric circles, and the determination of
- 43. About array processingmethods for image segmentation 25 each radius value. For this purpose we employ a variable speed propagation scheme (Aghajan & Kailath, 1994). We set 1 i µ , for each sensor indexed by S ,..., i 1 . From Eq. (12), the signal received on each sensor is: d k k S ,..., i , i n r i j exp i z 1 1 1 (13) where d ,..., k , rk 1 are the values of the radius of each circle, and i n is a noise term that can appear because of the presence of outliers. All components i z compose the observation vector z . TLS-ESPRIT method is applied to estimate d ,..., k , rk 1 , the number of concentric circles d is estimated by MDL (Minimum Description Length) criterion. The estimated radius values are obtained with TLS-ESPRIT method, which also estimated straight line orientations (see section 2.2). To retrieve the distortions between an expected star-shaped contour and a fitting circle, we work successively on each quarter of circle, and retrieve the distortions between one quarter of the initialization circle and the part of the expected contour that is located in the same quarter of the image. As an example, in Fig.3, the right bottom quarter of the considered image is represented in Fig. 3(b). The optimization method that retrieves the shift values between the fitting circle and the expected contour is the following: A contour in the considered sub-image can be described in a set of polar coordinates by : S ,..., i , i , i 1 . We aim at estimating the S unknowns S ,..., i , i 1 that characterize the contour, forming a vector: T S ,..., , 2 1 ρ (14) The basic idea is to consider that ρ can be expressed as: T S r ,..., r , r 2 1 ρ (see Fig. 3), where r is the radius of a circle that approximates the expected contour. 5. Linear and circular array for signal generation: summary In this section, we present the outline of the reviewed methods for contour estimation. An outline of the proposed nearly rectilinear distorted contour estimation method is given as follows: Signal generation with constant parameter on linear antenna, using Eq. 1; Estimation of the parameters of the straight lines that fit each distorted contour (see subsection 3.1); Distortion estimation for a given curve, estimation of x , applying gradient algorithm to minimize a least squares criterion (see Eq. 11). The proposed method for star-shaped contour estimation is summarized as follows: Variable speed propagation scheme upon the proposed circular antenna : Estimation of the number of circles by MDL criterion, estimation of the radius of each circle fitting any expected contour (see Eqs. (12) and (13) or the axial parameters of the ellipse; Estimation of the radial distortions, in polar coordinate system, between any expected contour and the circle or ellipse that fits this contour. Either the
- 44. Recent Advances inSignal Processing 26 gradient method or the combination of DIRECT and spline interpolation may be used to minimize a least-squares criterion. Table 1 provides the steps of the algorithms which perform nearly straight and nearly circular contour retrieval. Table 1 provides the directions for signal generation, the parameters which characterize the initialization contour and the output of the optimization algorithm. Table 1. Nearly straight and nearly circular distorted contour estimation: algorithm steps. The current section presented a method for the estimation of the radius of concentric circles with a priori knowledge of the center. In the next section we explain how to estimate the center of groups of concentric circles. 6. Linear antenna for the estimation of circle center parameters Usually, an image contains several circles which are possibly not concentric and have different radii (see Fig. 5). To apply the proposed method, the center coordinates for each feature are required. To estimate these coordinates, we generate a signal with constant propagation parameter upon the image left and top sides. The th l signal component, generated from the th l row, reads: N m lin jµm exp m , l I l z 1 where µ is the propagation parameter. The non-zero sections of the signals, as seen at the left and top sides of the image, indicate the presence of features. Each non-zero section width in the left (respectively the top) side signal gives the height (respectively the width) of the corresponding expected feature. The middle of each non-zero section in the left (respectively the top) side signal yields the value of the center c l (respectively c m ) coordinate of each feature.
- 45. About array processingmethods for image segmentation 27 Fig. 5. Nearly circular or elliptic features. r is the circle radius, a and b are the axial parameters of the ellipse. 7. Combination of linear and circular antenna for intersecting circle retrieval We propose an algorithm which is based on the following remarks about the generated signals. Signal generation on linear antenna yields a signal with the following characteristics: The maximum amplitude values of the generated signal correspond to the lines with maximum number of pixels, that is, where the tangent to the circle is either vertical or horizontal. The signal peak values are associated alternatively with one circle and another. Signal generation on circular antenna yields a signal with the following characteristics: If the antenna is centered on the same center as a quarter of circle which is present in the image, the signal which is generated on the antenna exhibits linear phase properties (Marot & Bourennane, 2007b) We propose a method that combines linear and circular antenna to retrieve intersecting circles. We exemplify this method with an image containing two circles (see Fig. 6(a)). It falls into the following parts: Generate a signal on a linear antenna placed at the left and bottom sides of the image; Associate signal peak 1 (P1) with signal peak 3 (P3), signal peak 2 (P2) with signal peak 4 (P4); Diameter 1 is given by the distance P1-P3, diameter 2 is given by the distance P2- P4; Center 1 is given by the mid point between P1 and P3, center 2 is given by the mid point between P2 and P4; Associate the circular antenna with a sub-image containing center 1 and P1, perform signal generation. Check the phase linearity of the generated signal; Associate the circular antenna with a sub-image containing center 2 and P4, perform signal generation. Check the linearity of the generated signal. Fig. 6(a) presents, in particular, the square sub-image to which we associate a circular antenna. Fig. 6(b) and (c) shows the generated signals.
- 46. Recent Advances inSignal Processing 28 Fig. 6. (a) Two intersecting circles, sub-images containing center 1 and center 2; signals generated on (b) the bottom of the image, (c) the left side of the image. 8. Results The proposed star-shaped contour detection method is first applied to a very distorted circle, and the results obtained are compared with those of the active contour method GVF (gradient vector flow) (Xu & Prince, 1997). The proposed multiple circle detection method is applied to several application cases: robotic vision, melanoma segmentation, circle detection in omnidirectional vision images, blood cell segmentation. In the proposed applications, we use GVF as a comparative method or as a complement to the proposed circle estimation method. The values of the parameters for GVF method (Xianghua & Mirmehdi, 2004) are the following. For the computation of the edge map: 100 iterations; 09 0, µGVF (regularization coefficient); for the snakes deformation: 100 initialization points and 50 iterations; 2 0. GVF (tension); 03 0. GVF (rigidity); 1 GVF (regularization coefficient); 8 0. GVF (gradient strength coefficient). The value of the propagation parameter values for signal generation in the proposed method are 1 µ and 3 10 5 . 8.1 Hand-made images In this subsection we first remind a major result obtained with star-shaped contours, and then proposed results obtained on intersecting circle retrieval. 8.1.1 Very distorded circles The abilities of the proposed method to retrieve highly concave contours are illustrated in Figs. 7 and 8. We provide the mean error value over the pixel radial coordinate E M . We notice that this value is higher when GVF is used, as when the proposed method is used.
- 47. About array processingmethods for image segmentation 29 Fig. 7. Examples of processed images containing the less (a) and the most (d) distorted circles, initialization (b,e) and estimation using GVF method (c,f). E M =1.4 pixel and 4.1 pixels. Fig. 8. Examples of processed images containing the less (a) and the most (d) distorted circles, initialization (b,e) and estimation using GVF method (c,f). E M =1.4 pixel and 2.7 pixels.
- 48. Recent Advances inSignal Processing 30 8.1.2 Intersecting circles We first exemplify the proposed method for intersecting circle retrieval on the image of Fig. 9(a), from which we obtain the results of Fig. 9(b) and (c), which presents the signal generated on both sides of the image. The signal obtained on left side exhibits only two peak values, because the radius values are very close to each other. Therefore signal generation on linear antenna provides a rough estimate of each radius, and signal generation on circular antenna refines the estimation of both values. The center coordinates of circles 1 and 2 are estimated as 41 83 1 1 , m , l c c and 84 83 2 2 , m , l c c . Radius 1 is estimated as 24 1 r , radius 2 is estimated as 30 2 r . The computationally dominant operations while running the algorithm are signal generation on linear and circular antenna. For this image and with the considered parameter values, the computational load required for each step is as follows: signal generation on linear antenna: 2 10 8 3 . sec.; signal generation on circular antenna: 1 10 8 7 . sec. So the whole method lasts 1 10 1 8 . sec. For sake of comparison, generalized Hough transform with prior knowledge of the radius of the expected circles lasts 2.6 sec. for each circle. Then it is 6.4 times longer than the proposed method. Fig. 9. (a) Processed image; signals generated on: (b) the bottom of the image; (c) the left side of the image. The case presented in Figs. 10(a) and 10(b), (c) illustrates the need for the last two steps of the proposed algorithm. Indeed the signals generated on linear antenna present the same peak coordinates as the signals generated from the image of Fig. 7(a). However, if a subimage is selected, and the center of the circular antenna is placed such as in Fig. 7, the phase of the generated signal is not linear. Therefore, for Fig. 10(a), we take as the diameter values the distances P1-P4 and P2-P3. The center coordinates of circles 1 and 2 are estimated as 55 68 1 1 , m , l c c and 99 104 2 2 , m , l c c . Radius of circle 1 is estimated as 87 1 r , radius of circle 2 is estimated as 27 2 r .
- 49. About array processingmethods for image segmentation 31 Fig. 10. (a) Processed image; signals generated on: (b) the bottom of the image; (c) the left side of the image. Here was exemplified the ability of the circular antenna to distinguish between ambiguous cases. Fig. 11 shows the results obtained with a noisy image. The percentage of noisy pixels is 15%, and noise grey level values follow Gaussian distribution with mean 0.1 and standard deviation 0.005. The presence of noisy pixels induces fluctuations in the generated signals, Figs. 11(b) and 11(c) show that the peaks that permit to characterize the expected circles are still dominant over the unexpected fluctuations. So the results obtained do not suffer the influence of noise pixels. The center coordinates of circles 1 and 2 are estimated as 88 131 1 1 , m , l c c and 144 53 2 2 , m , l c c . Radius of circle 1 is estimated as 67 1 r , radius of circle 2 is estimated as 40 2 r . Fig. 11. (a) Processed image; signals generated on: (b) the bottom of the image; (c) the left side of the image. 8.2 Robotic vision We now consider a real-world image coming from biometrics (see Fig. 12(a)). This image contains a contour with high concavity. Fig. 12(b) gives the result of the initialization of our optimization method. Fig. 12(c) shows that GVF fails to retrieve the furthest sections of the narrow and deep concavities of the hand, that correspond to the two right-most fingers. Fig. 12(d) shows that the proposed method for distortion estimation manages to retrieve all pixel shift values, even the elevated
- 50. Recent Advances inSignal Processing 32 ones. We also noticed that the computational time which is required to obtain this result with GVF is 25-fold higher than the computational time required by the proposed method: 400 sec. are required by GVF, and 16 sec. are required by our method. Fig. 12. Hand localization: (a) Processed image, (b) initialization, (c) final result obtained with GVF, (d) final result obtained with the proposed method 8.3 Omnidirectionnal images Figures 13(a), (b), (c) show three omnidirectional images, obtained with a hyperbolic mirror. For some images it is useful to remove to parasite circles due to the acquisition system. The experiment illustrated on Fig. 14 is an example of characterization of two circles that overlap. Figures 14(a), (b), (c), show for one image the gradient image, the threshold image, the signal generated on the bottom side of the image (Marot & Bourennane, 2008). The samples for which the generated signal takes none zero values (see Fig. 14(c)) delimitate the external circle of Fig. 13(a). The diameter of the big circle is 485 pixels and the horizontal coordinate of its center is 252 pixels. This permits first to erase the external circle, secondly to characterize the intern circle by the same method. Fig. 13. Omnidirectional images
- 51. About array processingmethods for image segmentation 33 Fig. 14. Circle characterization by signal generation 8.4 Cell segmentation Fig. 15 presents the case of a real-world image. It contains one red cell and one white cell. Our goal in this application is to detect both cells. The minimum value in the signal generated on bottom side of the image corresponds to the frontier between both cells. The width of the non-zero sections on both sides of the minimum value is the diameter of each cell. Each peak value in each generated signal provides one center coordinate. Fig. 15. Blood cells: (a) processed image; (b) superposition processed image and result; signals generated on: (c) the bottom of the image; (d) the left side of the image. 8.5 Melanoma segmentation Fig. 16 concerns quantitative analysis in a medical application. More precisely, the purpose of the experiment is to detect the frontier of a melanoma. The melanoma was chosen randomly out of a database (Stolz et al., 2003).
- 52. Recent Advances inSignal Processing 34 Fig. 16. Melanoma segmentation: (a) processed image, (b) elliptic approximation by the proposed array processing method, (c) result obtained by GVF. The proposed array processing method detects a circular approximation of the melanoma borders (Marot & Bourennane, 2007b; Marot & Bourennane, 2008) (see Fig 16(b)). A few iterations of GVF method (Xu & Prince, 1997) yield the contour of the melanoma (see Fig 16(c)). Such a method can be used to control automatically the evolution of the surface of the melanoma. 9. Conclusion This chapter deals with contour retrieval in images. We review the formulation and resolution of rectilinear or circular contour estimation. The estimation of the parameters of rectilinear or circular contours is transposed as a source localization problem in array processing. We presented the principles of SLIDE algorithm for the estimation of rectilinear contours based on signal generation upon a linear antenna. In this frame, high-resolution methods of array processing retrieve possibly close parameters of straight lines in images. We explained the principles of signal generation upon a virtual circular antenna. The circular antenna permits to generate linear phase signals out of an image containing circular features. The same signal models as for straight line estimation are obtained, so high- resolution methods of array processing retrieve possibly close radius values of concentric circles. For the estimation of distorted contours, we adopted the same conventions for signal generation, that is, either a linear or a circular antenna. For the first time, in this book chapter, we propose an intersecting circle retrieval method, based on array processing algorithms. Signal generation on a linear antenna yields the center coordinates and radii of all circles. Circular antenna refines the estimation of the radii and distinguishes ambiguous cases. The proposed star-shaped contour estimation method retrieves contours with high concavities, thus providing a solution to Snakes based methods. The proposed multiple circle estimation method retrieves intersecting circles, thus providing a solution to levelset- type methods. We exemplified the proposed method on hand-made and real-world images. Further topics to be studied are the robustness to various types of noise, such as correlated Gaussian noise.
- 53. About array processingmethods for image segmentation 35 10. References Abed-Meraim, K. & Hua, Y. (1997). Multi-line fitting and straight edge detection using polynomial phase signals, ASILOMAR31, Vol. 2, pp. 1720-1724, 1997. Aghajan, H. K. & Kailath, T. (1992). A subspace Fitting Approach to Super Resolution Multi- Line Fitting and Straight Edge Detection, Proc. of IEEE ICASSP, vol. 3, pp. 121-124, 1992. Aghajan, H. K. & Kailath, T. (1993a). Sensor array processing techniques for super resolution multi-line-fitting and straight edge detection, IEEE Trans. on IP, Vol. 2, No. 4, pp. 454-465, Oct. 1993. Aghajan, H.K. & Kailath, T. (1993b). SLIDE: subspace-based line detection, IEEE int. conf. ASSP, Vol. 5, pp. 89 - 92, April 27-30, 1993. Aghajan, H. & Kailath, T. (1995). SLIDE: Subspace-based Line detection, IEEE Trans. on PAMI, 16(11):1057-1073, Nov. 1994. Aghajan, H.K. (1995). Subspace Techniques for Image Understanding and Computer Vision, PhD Thesis, Stanford University, 1995 Bourennane, S. & Marot, J. (2005). Line parameters estimation by array processing methods, IEEE ICASSP, Vol. 4, pp. 965-968, Philadelphie, Mar. 2005. Bourennane, S. & Marot, J. (2006a). Estimation of straight line offsets by a high resolution method, IEE proceedings - Vision, Image and Signal Processing, Vol. 153, issue 2, pp. 224-229, 6 April 2006. Bourennane, S. & Marot, J. (2006b). Optimization and interpolation for distorted contour estimation, IEEE-ICASSP, vol. 2, pp. 717-720, Toulouse, France, April 2006. Bourennane, S. & Marot, J. (2006c). Contour estimation by array processing methods, Applied signal processing, article ID 95634, 15 pages, 2006. Bourennane, S.; Fossati, C. & Marot, J., (2008). About noneigenvector source localization methods EURASIP Journal on Advances in Signal Processing Vol. 2008, Article ID 480835, 13 pages doi:10.1155/2008/480835 Brigger, P. ; Hoeg, J. & Unser, M. (2000). B-Spline Snakes: A Flexible Tool for Parametric Contour Detection, IEEE Trans. on IP, vol. 9, No. 9, pp. 1484-96, 2000. Cheng, J. & Foo, S. W. (2006). Dynamic directional gradient vector flow for snakes, IEEE Trans. on Image Processing, vol. 15, no. 6, pp.1563-1571, June 2006. Connell, S. D. & Jain, A. K. (2001). Template-based online character recognition, Pattern Rec., vol. 34, no 1, pp: 1-14, 2001. Gander, W.; Golub, G.H. & Strebel, R. (1994). Least-squares fitting of circles and ellipses , BIT, n. 34, pp. 558-578, 1994. Halder, B. ; Aghajan, H. & T. Kailath (1995). Propagation diversity enhancement to the subspace-based line detection algorithm, Proc. SPIE Nonlinear Image Processing VI Vol. 2424, p. 320-328, pp. 320-328, March 1995. Jones, D.R. ; Pertunen, C.D. & Stuckman, B.E. (1993). Lipschitzian optimization without the Lipschitz constant, Journal of Optimization and Applications, vol. 79, no. 157-181, 1993. Karoui, I.; Fablet, R.; Boucher, J.-M. & Augustin, J.-M. (2006). Region-based segmentation using texture statistics and level-set methods, IEEE ICASSP, pp. 693-696, 2006. Kass, M.; Witkin, A. & Terzopoulos, D. (1998). Snakes: Active Contour Model, Int. J. of Comp. Vis., pp.321-331, 1988 Kiryati, N. & Bruckstein, A.M. (1992). What's in a set of points? [straight line fitting], IEEE Trans. on PAMI, Vol. 14, No. 4, pp.496-500, April 1992.
- 54. Recent Advances inSignal Processing 36 Marot, J. & Bourennane, S. (2007a). Array processing and fast Optimization Algorithms for Distorted Circular Contour Retrieval , EURASIP Journal on Advances in Signal Processing, Vol. 2007, article ID 57354, 13 pages, 2007. Marot, J. & Bourennane, S. (2007b). Subspace-Based and DIRECT Algorithms for Distorted Circular Contour Estimation, IEEE Trans. On Image Processing, Vol. 16, No. 9, pp. 2369-2378, sept. 2007. Marot, J., Bourennane, S. & Adel, M. (2007). Array processing approach for object segmentation in images, IEEE ICASSP'07, Vol. 1, pp. 621-24, April 2007. Marot, J. & Bourennane, S. (2008). Array processing for intersecting circle retrieval, EUSIPCO'08, 5 pages, Aug. 2008. Marot, J.; Fossati, C.; & Bourennane, S. (2008) Fast subspace-based source localization methods IEEE-Sensor array multichannel signal processing workshop, Darmstadt Germany, 07/ 2008 Osher, S. & Sethian, J. (1998). Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. , Vol. 79, pp. 12-49, 1988. Paragios, N. & Deriche, R. (2002). Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation, Int'l Journal of Computer Vision, Vol. 46, No 3, pp. 223-247, Feb. 2002. Pillai, S.U. & Kwon, B.H. (1989). Forward/backward spatial smoothing techniques for coherent signal identification, Proc. of IEEE trans. on ASSP, vol. 37 (1), pp. 8-15, 1989. Precioso, F. ; Barlaud, M. ; Blu, T. & Unser, M. (2005). Robust Real-Time Segmentation of Images and Videos Using a Smooth-Spline Snake-Based Algorithm, IEEE Trans. on IP, Vol. 14, No. 7, pp. 910-924, July 2005. Roy, R. & Kailath, T. (1989). ESPRIT: Estimation of signal parameters via rotational invariance techniques, IEEE Trans. on ASSP, vol. 37, no. 7, pp. 984-995, 1989. Sheinvald, J. & Kiryati,N. (1997). On the Magic of SLIDE, Machine Vision and Applications, Vol. 9, pp. 251-261, 1997. Stolz, W. ; Horsch, A. ; Pompl, R. ; Abmayr, W. ; Landthaler, M. (2003) Datensatz Dermatology Skin Surface Microscopy Melanocytic Lesions 749, Version 1.0, October 2003 (D-SSM-ML-749 V1.0). Tufts, D.W. & Kumaresan, R. (1982). Estimation of frequencies of multiple sinusoids: making linear prediction perform like maximum likelihood, Proc. IEEE, vol. 70, pp. 975-989, sept. 1982. Unser, M. ; Aldroubi, A. & Eden, M. (1993). B-spline signal processing: Part I-theory; part II- efficient design and applications, IEEE Trans. on SP, Vol. 41, No. 2, pp. 821-848, Feb. 1993. Xianghua X. & Mirmehdi, M. (2004). RAGS: region-aided geometric snake , IEEE Trans. IP, Vol. 13, no. 5, pp: 640-652, May 2004. Xu, C. & Prince, J.L. (1997). Gradient vector flow: a new external force for snakes, Proceeding of IEEE Computer Society Conference on Computer -Vision and Pattern Recognition pp. 66-71, Jun. 1997. Zhu, S. C. & Yuille, A. (1996). Region Competition: Unifying Snakes, Region Growing, and Bayes /MDL for Multiband Image Segmentation, IEEE Trans. on PAMI, Vol. 18, No. 9, pp. 884-900, Sept. 1996.
- 55. Exploring the Varietyof Random Documents with Different Content
- 56. “No, of courseI never love you any less. Did the time seem long to you while I was away?” “Oh! yes, mamma! But luckily I have had a new maid for three weeks. Father must have written you that he discharged the other one, didn’t he?” “Yes, dear.” “Oh! I like the new one ever so much better! If you knew how nice she is! and not a bit stupid, nor vulgar! She speaks very correctly, and yet she came right from her village; she has never lived out, but she learned her duties instantly.” “Who brought her here?” “Comtois. He had excellent recommendations.” Madame de Noirmont smiled at the serious tone in which her daughter spoke. “My dear girl,” she replied, “I know that we may rely on Comtois.— What is your new maid’s name?” “Louise—Louise Fré—Frénet—I never can remember her other name. But no matter, she’s a very nice girl, I tell you, mamma; I am sure that you will like her too. I am going to call her, to show her to you. She’s very shy, that is why she hasn’t come to pay her respects to you.” “Mon Dieu! my dear love, I have plenty of time to see your maid; there is no hurry about it.” “Oh, yes! I want you to see her right away, mamma.” Ernestine rang a bell; in a moment the door opened and Louise appeared in the doorway, timid and with downcast eyes. “Did madame ring for me?” she murmured. Madame de Noirmont scrutinized the girl, whom she then saw for the first time; she was struck by her beauty, by the dignified expression of her features, by her modest and reserved demeanor, by her whole aspect, which was not what one ordinarily sees in a lady’s maid. She could not tire of looking at her. Ernestine leaned toward her mother and whispered: “Well! what do you think of her?” “Lovely, my child, lovely; she has an air of distinction too; no one would think that she was a servant.”
- 57. “I didn’t flatterher, did I?—Mamma thinks that you are lovely, Louise,” continued the girl; “she likes you too. I told you that she would like you.” Louise made a curtsy and murmured: “Madame is very kind; I will do my best to satisfy her, and mademoiselle too.” “I don’t doubt it, my child,” replied Madame de Noirmont; “everything prepossesses me in your favor, and I am convinced that my daughter is not mistaken in all the good that she has told me of you.” While Ernestine’s mother was speaking, Louise raised her eyes and looked at her. At sight of that beautiful, noble and stern face, of that pale and haughty brow, of those great black eyes wherein one could always detect a melancholy expression, the girl felt deeply moved and impressed; her heart beat violently, whether with pleasure or fear she did not know; she could not define her feelings, but she did not speak or move. For some moments after Madame de Noirmont ceased speaking, she continued to listen; they motioned to her that she might retire, and she remained. At last Ernestine had to touch her arm and say: “You may leave us, Louise,” before she came to herself and left the room, casting a last furtive glance at Madame de Noirmont. After a few more words concerning the new lady’s maid, Madame de Noirmont turned all her attention to taking up the threads of her usual domestic occupations, and to superintending her daughter’s education and her studies with the different teachers who came to the house to give her lessons. Madame de Noirmont’s life was very regular; she rarely went out and received few visits; she devoted herself to her daughter, overlooked her studies and read a great deal: that was her greatest pleasure, her most agreeable means of distraction. Monsieur de Noirmont passed the whole day in his study; his wife and daughter saw little of him before dinner. At that repast they met, and not infrequently some old friend of Monsieur de Noirmont dined with them, but they very rarely had more than one guest. During dinner Madame de Noirmont talked very little, while her husband discussed politics or economic matters with his guest. Ernestine alone did anything to enliven the party. She succeeded very well; her childish sallies and observations often made her mother smile; and even Monsieur de Noirmont, despite his
- 58. gravity, could notalways keep a sober face. In the evening, the ladies worked, made tapestry, or sang, and the men played chess or backgammon. When there were no guests at dinner, Monsieur de Noirmont often went out in the evening to some party or reception; sometimes his wife and daughter accompanied him, but rarely. Madame de Noirmont preferred to remain at home with Ernestine; and when her husband was not there, she seemed less serious, less pensive, and she manifested her affection for Ernestine more freely. Louise’s duties were very pleasant in that family, where the ladies did not go to balls and received very little company. Comtois alone waited at table. The young lady’s maid assisted the ladies to dress; then, during almost all the remainder of the day, she worked in her room, making dresses for mademoiselle or keeping the linen of the household in order. In the evening, she served at tea, then looked to it that her mistresses had everything in their room that they required. This was not very wearisome, and Louise sometimes told Ernestine that they did not give her enough work to do; but the girl would reply, with a smile: “What makes you work so fast? We no sooner give you a piece of sewing to do than it is done. Mamma says that your activity and skill are most unusual. Other lady’s maids don’t work so fast, I promise you!” Louise felt a thrill of pleasure whenever she was told that Madame de Noirmont was pleased with her. And although that lady always preserved a grave and serious manner with her servants, which made the slightest approach to familiarity impossible, she felt drawn to love her, and it seemed to her that it would be a source of deep grief to her if she should now be compelled to leave her. Meanwhile three months had passed since she came to Paris, and she had not once seen Chérubin. But since Madame de Noirmont’s return, Louise, engrossed by the desire to please her, had felt her love-pangs less sharply; although she still loved her old playmate as dearly as ever, another sentiment had glided into her heart, to distract her thoughts from her troubles. Monsieur Gérondif had called several times to inquire of Comtois what Louise’s employers thought of her, and each time the old servant put forth all his eloquence in praise of the young lady’s maid and begged the professor to thank old Jasmin for the present he had sent them. Monsieur
- 59. Gérondif went awayoverjoyed that he had brought Louise to Paris, although Chérubin, entirely absorbed by his bonnes fortunes, had forgotten about going to see Nicole. One morning, when Monsieur Gérondif called at Monsieur de Noirmont’s to ask Comtois if they were still content with Louise, the valet replied: “Yes, indeed; Mademoiselle Louise is a model of virtue and industry. If you would like to see her, monsieur, she is alone at this moment; the ladies have gone out to do some shopping. She is working in her room, and there is no reason why you should not go up and bid her good-morning.” Monsieur Gérondif joyfully accepted the proposition; he followed Comtois, who led him to Louise’s chamber and left him with her. Louise manifested the keenest delight at sight of the tutor, for she would have an opportunity to talk with him about all those who were dear to her. Monsieur Gérondif, who was, like most pedants, a conceited fool, took to himself a pleasure of which he was the pretext simply; he believed that he had kindled a tender sentiment in the breast of the pretty lady’s maid, and he smiled as if he would dislocate his jaw as he took his seat beside her. Louise began by inquiring for her adopted mother. “She is perfectly well, and she is overjoyed that you are in such a fine position in Paris,” replied the tutor, lying with imperturbable coolness; for he had not been to the village since Louise left it. “And Monsieur Chérubin?” continued Louise, “is he pleased to know that I am in Paris as he wished? Hasn’t he any desire to see me? Doesn’t he ever speak to you about me? Did he send you here to-day?” The tutor scratched his nose, coughed, spat, wiped his forehead, all of which operations required much time with him, during which he considered what he should say. Having made up his mind at last, he said to Louise: “My dear child, it rarely happens that childish loves come to a good end. I might cite Paul and Virginie and a thousand other examples ad hoc; I prefer to tell you ex abrupto—which means, without preamble—that you are making a mistake to give any further thought to Monsieur le Marquis de Grandvilain, because that young man never gives a thought to you. In the first place, when you came to see him at his house—when you came to Paris with Nicole——”
- 60. “Well, monsieur?” “Well, theyoung marquis was at home; but as he didn’t want to see you, he gave his concierge orders to tell you that he was away.” “O mon Dieu! is it possible?” “Amid the debauchery in which he is plunged, how do you expect him to remember a young country girl with whom he used to play puss-in-the- corner, and other more or less innocent games? He has become a great rake, has my pupil; he has a lot of mistresses. It isn’t my fault. He receives so many billets-doux that it’s perfectly scandalous, and I should have left his house before this if my financial interests did not oblige me to close my eyes,—which however, does not prevent my seeing whatever happens.” Louise put her handkerchief to her eyes and faltered: “So it’s all over—he doesn’t love me at all! Who would have believed it of Chérubin?” “One must believe everything, expect everything from a beardless youth,” replied the tutor. Then, drawing his chair close to the girl’s, and laying his hand on her knee, Monsieur Gérondif tried to assume a mellifluous voice and began, weighing his words: “I have made the wound, and it is for me to apply the balsam, otherwise called the remedy.—Lovely Louise, although young Chérubin has not been true to your charms, there are others who will be too happy to offer incense to them, to cultivate them. I go straight to the point: I love you, divine maiden! and I am not fickle, because, thank heaven, I am a grown man. I have not come to make any base propositions to you—retro, Satanas! which means: I have only honorable views. I offer you my hand, my heart, my name, my rank and my title; but we will wait two years before we marry. I will try to restrain my passions for that length of time, which I require in order to amass a tidy sum of money. You will contribute your wages, your savings; they are much pleased with you here, and it is probable that you will receive a handsome present at New Year’s. We will put it all together and buy a little house in the outskirts of Paris; I will take a few pupils to keep my hand in; we will have a dog, a cat, chickens, all the pleasant things of life, and our days will be blended of honey and hippocras.”
- 61. During this harangue,Louise had pushed away the hand that Monsieur Gérondif had laid on her knee, and had moved her chair away; and as soon as he had finished speaking, she rose and said to him in a courteous but determined tone: “I thank you, monsieur, for condescending to offer me, a poor village girl, without name or family, the title of your wife; but I cannot accept it. Monsieur Chérubin no longer loves me; I can understand that, monsieur, and indeed I was mad to imagine that, in Paris, in the midst of pleasures, living in the whirl of society, he would remember me. But it is altogether different with me! I have not become a great lady, and the image of the man I love can never be effaced from my heart. I love Chérubin; I feel that I shall never love anybody else! So, monsieur, it would be very wicked of me to marry another man, as I could not give that other my love.” Monsieur Gérondif was greatly surprised by this speech; he recovered himself, however, and replied: “My sweet Louise, varium et mutabile semper femina; or, if you prefer: 'souvent femme varie, bien fol est qui s’y fie.’—Woman changes ever; he is a great fool who trusts her.—The latter lines are by François I; I prefer Beranger’s.—Tiresias declares that men have only three ounces of love, while women have nine, which enables them to change oftener than we do; and yet, with only three ounces, we do pretty well.” “What does all this mean, monsieur?” “It means, my dear love, that you will do like the others: you will change; your love will pass away.” “Never, monsieur.” “Never is a word that means nothing at all in love. However, you will have plenty of time to think about it, as I give you two years for reflection. Until then, allow me to hope.” “Oh! it is useless, monsieur.” “I beg pardon; by hoping one lives content, and I cling to my hope. Adieu, fair Louise; continue to behave becomingly; your remuneration will be increased doubtless, and I shall continue to put mine aside; and, as a very trivial but very shrewd popular proverb says: ‘Let’s let the mutton boil!’—I lay my homage at your feet.”
- 62. Monsieur Gérondif tookhis leave, and Louise was at liberty to weep without restraint. She did not bestow a thought on the tutor’s offers, she thought only of Chérubin, who no longer loved her, who had ceased to think of her, and who had mistresses. She had been afraid for a long time that he had forgotten her; but now she was certain of it, and it is a far cry from fear to certainty, in love. The return of Madame de Noirmont and her daughter forced Louise to conceal her tears. She hastily wiped her eyes and tried to dissemble her depression, for she felt that she must not betray the secret of her heart. On that day Monsieur de Noirmont went out after dinner. Ernestine remained with her mother, to whom, as they worked, she said whatever came into her head, especially as she saw that it was one of her moments of good humor. When Madame de Noirmont smiled at her daughter’s speeches, the latter was so delighted that she often laid her work aside to throw her arms about her mother’s neck, who sometimes held her lovingly to her heart for some moments. Louise, for whom they rang to order tea, entered the salon at one of the times when Madame de Noirmont’s arms were about her daughter; and the sweet child, in her joy at being so fondled, cried out: “See how happy I am, Louise! see what a dear, good mother I have!” Louise stood still in the middle of the salon; she was glad for Ernestine’s happiness, and yet, in the touching picture before her eyes, there was something that hurt her, she did not understand why. Two great tears escaped from her eyes; but she turned quickly, so that they might not see her weeping. Meanwhile Madame de Noirmont had resumed her grave demeanor, and Ernestine had had to return to her seat. Louise served the tea as quickly as possible, then left the room, fearing that her sadness would be noticed. Despite all her efforts to be calm, Louise was still crying when Ernestine entered her room to ask her some question, before going to bed. Seeing that Louise’s face was wet with tears, her young mistress ran to her, and said with the most touching interest: “Mon Dieu! crying, Louise! What’s the matter?” “Oh! excuse me, mademoiselle. I know that I should not weep here, where everyone is so kind to me; but I could not help it!”
- 63. “Have you somereason for being unhappy? You would not cry like this for nothing. Louise, I insist on knowing why you were crying.” “Well, mademoiselle, it is because, when I saw you in your mother’s arms to-night, the picture of the happiness you enjoy made me feel more keenly than ever the misery of my position. Oh! mademoiselle, it isn’t envy that makes me say it! I bless Heaven for making you so happy; but I could not help crying when I remembered that my mother never kissed me, that I shall never be able to throw my arms about her!” “What’s that you say, my poor Louise? Doesn’t your mother love you?” “It isn’t that, mademoiselle. But listen, I am going to tell you the truth, for I don’t know how to lie. And then, I don’t understand why I should make a mystery of it; you won’t be any less kind to me when you know that I am a poor girl, abandoned by her parents.” “Is it possible? you haven’t any parents?” “At all events, mademoiselle, I don’t know them.” Thereupon Louise proceeded to tell Ernestine the story of how Nicole had been employed to take care of her, and of the kindness of the village people, who had kept her and treated her like their daughter, when they found that she was abandoned by her mother. Ernestine listened to the story with the deepest interest. When Louise had ceased to speak, she kissed her affectionately, saying: “Poor Louise! Oh! how glad I am you have told me that! It seems to me that I love you even more since I know that your parents have abandoned you. And that dear, good Nicole! those kind peasants! Ah! what splendid people they are! I will tell mamma all about it to-morrow! I am sure that it will interest her too.” “Oh! that isn’t worth while, mademoiselle; Madame de Noirmont may not like it because I have told you about my troubles.” “I assure you, on the contrary, that, for all her serious manner, mamma is kind and good; and, besides, she likes you very much. She has said to me several times that your manners were just what they should be, and that is great praise from her, I tell you!—Well, good-night, Louise, sleep soundly, and don’t cry any more. If you haven’t any parents, you have some people here who love you dearly and who will take good care of you.”
- 64. Ernestine left Louise,to go to bed, and the latter felt less unhappy when she saw her young mistress’s affection for her—an affection which she shared with all the sincerity of her soul. The next morning the Noirmont family met at the breakfast table. Ernestine had not seen her mother since the preceding night, because a headache had kept Madame de Noirmont in bed later than usual; but her father, who rarely appeared at breakfast, had just taken his seat, when Ernestine, after kissing her mother, said in a mysterious tone: “I have something very interesting to tell you this morning, and I am glad papa came to breakfast, to hear what I am going to say.” “Really?” said Monsieur de Noirmont, smiling, and in a tone of mild raillery. “From the way in which you say that, I imagine that it must really be something most serious.” “Why, yes, papa, it’s very serious! Oh! you look as if you were laughing at me, but when you know what it is, I’ll bet that you will be as touched as I was last night when I found poor Louise crying!” “What! is it something about Louise?” asked Madame de Noirmont, with an air of deep interest; “can it be that anything has gone wrong with her? I should be extremely sorry, for the girl is a very good girl indeed, and seems to deserve our kindness.” “This is what it is; listen. Louise didn’t want me to tell you; but I am very sure that you won’t blame her for it; it isn’t her fault.” Monsieur de Noirmont, whose interest was aroused by this exordium, said impatiently: “Come, my child, go on, explain yourself.” “Well, papa, last evening, when Louise came to the salon to serve the tea, she found me in mamma’s arms, and we were kissing each other.” “That is well, my daughter; what next?” “At night, when I went up to bed, as I couldn’t find a fichu that I wanted, I went to Louise’s room to ask her where she had put it. I found her crying hard, and I asked her why she was crying. She replied, sobbing: ‘Oh! mademoiselle, because, when I saw you in your mother’s arms to-night, I felt more keenly than ever my misfortune in never having been kissed by my mother, and in being only an abandoned child.’”
- 65. “An abandoned child!”murmured Madame de Noirmont, whose face instantly became deathly pale. “But,” said Monsieur de Noirmont, “if I am not mistaken, Comtois told us that the girl’s parents lived in the outskirts of Paris—I don’t remember in what village.” “Yes, papa, that is what Comtois was told when Louise was brought here; but that was a lie that her friends thought they ought to tell. Louise thought it was better to tell the truth.” “She is right. But call your maid, Ernestine; I want to hear the whole story from her own lips. It has roused my curiosity. And you, madame—are not you curious to hear this girl’s story?” Madame de Noirmont replied with a few almost unintelligible words; it was as if she were oppressed by some secret suffering, which she was doing her utmost to conceal. Meanwhile, Ernestine had not waited for her father to repeat his request; she had run off to call Louise, who soon appeared before the assembled family. Monsieur de Noirmont looked at her with more interest than he had previously displayed; Ernestine smiled at her affectionately; Madame de Noirmont lowered her eyes and became paler than ever. From the disquietude that had taken possession of her, from the anxiety that could be read upon her features, one would have taken her for a criminal awaiting judgment. “Come, Louise, come nearer,” said Monsieur de Noirmont, motioning to her; “my daughter has told us of what you told her last evening. Do not tremble, my child; we shall not reproach you for telling us what was not true when you entered our service.” “Oh! it was not I, monsieur!” murmured Louise. “I know it, it was the person who obtained the situation for you, who thought it his duty to tell that falsehood.—So you do not know your parents, my poor girl?” “No, monsieur.” “Where were you brought up?” “At Gagny, monsieur.”
- 66. “At Gagny. Ah!that’s it; I had forgotten the name of the village that you told me when you came here.—And the people who brought you up?” “A kindhearted peasant woman, Nicole Frimousset. She was nursing Monsieur Chérubin de Grandvilain at the time.” “Indeed! so this woman was the young Marquis de Grandvilain’s nurse?” “Yes, monsieur, he is my foster-brother, and in my childhood we played together all the time.” “Very good! But that doesn’t tell us how you went to Gagny.” “Mon Dieu! monsieur, it was a lady—my mother, I suppose—who carried me to dear Nicole’s, and begged her to take me to nurse. I was then a year old; she left some money with Nicole and went away, saying that she would come again. The next year she sent a little more money by a messenger from Paris; but she didn’t come to see me, and no one ever after came to inquire for me.” “But what was the lady’s name; where did she live?” “Nicole didn’t think to ask her any of those questions; for she could not dream that she would abandon me, that she would never come again. The messenger from Paris did not know who the lady was who hired him on the street, he could not tell my good nurse anything.” “But was no paper, no mark found on you or on your clothing?” “Nothing, monsieur, absolutely nothing.” “That is very strange.—Don’t you agree with me, madame?” As he asked this question Monsieur de Noirmont turned to his wife, whom he had not looked at while questioning Louise; Ernestine, whose eyes followed her father’s, uttered a piercing shriek. “Oh dear!” she cried, “mamma has fainted!” Madame de Noirmont’s head had fallen against the back of her chair; she had in fact lost consciousness, and the livid pallor of her face made her condition seem most alarming. They hastened to her assistance; Ernestine wept and lamented as she kissed her mother again and again. Louise shared her distress; she lost her head, did not know what to do, and did not hear what was said to her. But Monsieur de Noirmont, who retained all his presence of mind, called
- 67. Comtois, and, withhis assistance, carried his wife to her room and laid her on her bed. After some time, Madame de Noirmont came to herself; but there was a look of gloom and anxiety in her eyes, which indicated that the cause of her trouble still existed. She turned her eyes slowly on her husband and her daughter; then, as she caught sight of Louise, who was a little farther away and who seemed to share the general anxiety, she closed her eyes and let her head fall back on the pillow. “Mamma, dear mamma, how do you feel now?” cried Ernestine, squeezing her mother’s hand. “Better, my dear, I feel better.” “What was the cause of your sudden illness, madame?” asked Monsieur de Noirmont with interest. “You gave us a terrible fright.” “Why, I have no idea, monsieur. I had a sudden feeling of suffocation; then a cold perspiration broke out all over me, and I lost the use of my senses.” “You didn’t feel well this morning, you had a headache,” said Ernestine. “Yes, that is true,” replied Madame de Noirmont hastily. “I felt poorly this morning, and that is the cause, no doubt——” “And then Louise’s story must have grieved you, made your heart ache. That probably made you worse.” “Do you wish me to send for the doctor, madame?” “No, monsieur, it is not necessary; I need nothing but rest and quiet— and a little sleep, perhaps.” “We will leave you, then.” “But I shall be close by,” said Ernestine, “and I will come at the slightest sound.” Madame de Noirmont seemed most desirous to be left alone. All the others went away, Ernestine still deeply moved because she had seen her mother in a swoon, and Louise very much cast down because she feared that the story of her misfortunes had touched her mistress too deeply. Madame de Noirmont passed the rest of the day in her room; she kept her bed and expressed a wish to be alone. The next day passed in the same way; and for several days she did not leave her bed.
- 68. She refused tosee a doctor, however, and declared that her trouble required no other remedy than rest. But from the first moment of her illness, it was evident that Madame de Noirmont’s humor had changed: she hardly spoke; sometimes her daughter’s presence seemed irksome to her; she answered her curtly and received her caresses without warmth. As for Louise, while her mistress kept her room, she persistently declined her services on the pretext that she did not require them. Poor Louise was greatly distressed. “Madame your mother,” she said to Ernestine, “will not let me wait on her, or even go into her room. I am afraid that I have displeased her, mademoiselle; perhaps she does not like to have in her house a girl whose parents are not known.” Ernestine tried to comfort her, saying: “You are wrong. Why should you think that mamma has anything against you? No, it is this trouble of hers, it’s her nerves that make her depressed and irritable. Why, she even pushes me away now when I kiss her, and she doesn’t kiss me; that makes me unhappy too, but I am sure that mamma still loves me.” As she spoke, the sweet child shed tears, and Louise mingled hers with them, for she could think of no other consolation to give her. Madame de Noirmont made up her mind at last to leave her room, and she went down to the salon. The first time that Louise saw her, she longed to ask about her health, but she dared not; her mistress’s eyes seemed to avoid hers, and she did not display her former kindliness to her. For the merest trifle, Madame de Noirmont lost patience, scolded and became angry; sometimes she gave Louise ten contradictory orders in the same minute. The poor girl lost her head, was bewildered, did not know what to do, while Ernestine gazed at her mother with a surprised and grieved expression, when she saw her treat her protégée so harshly. Sometimes, however, a violent change seemed to take place in that strange creature; after speaking sharply and severely to Louise, Madame de Noirmont, remarking the poor girl’s heartbroken expression, would suddenly change her tone; her eyes would fill with tears and follow Louise’s every movement; then she would call her in a gentle, affectionate, even tender voice, and the girl would return instantly, joyous and eager; but
- 69. her mistress’s facewould already have resumed its stern expression, and she would motion her away, muttering curtly: “What do you want? I didn’t call you.” Several weeks passed in this way. One morning, Madame de Noirmont, who seemed even more thoughtful than usual, said to her daughter when she came to kiss her: “Really, I don’t propose to keep your maid; the girl is good for nothing; we must dismiss her. We will pay her two or three months’ wages more than is due her. Tell her, and advise her to return to her village; I think that she made a great mistake in coming to Paris to seek employment. Do not try to change my decision, it would do no good.” Ernestine was in despair; she was very fond of Louise, and it would be a real sorrow to her to part with her; but her mother had spoken in such a stern and decided tone that the poor child dared not reply. She said nothing, but lowered her eyes with a sigh, and left the room to perform the distressing duty with which her mother had entrusted her. As she left her mother’s apartment, Ernestine met Monsieur de Noirmont, who came up to her and kissed her, and said, observing her sorrowful air: “What is it, my child? You look as if you had been crying!” “It’s nothing, papa.” “You know, Ernestine, that I do not like evasions or mysteries; I insist upon knowing at once what makes you unhappy this morning.” “Well, papa, it’s because mamma is going to send Louise away, poor Louise, our maid, who is so sweet, and whom I love so dearly. But mamma doesn’t like her any more; she says that Louise isn’t good for anything; but Louise works just as much as she ever did, and she sews like an angel. But as mamma insists, I am going to tell Louise, so that she——” “Don’t go to her, my child, it is not necessary; Louise will stay in this house.” “But, papa, when mamma told me——” “I tell you the opposite, my child, and I am the only master here.” Ernestine said no more, for her father had assumed a severe expression which in him denoted that he had formed a resolution which no one could change. Monsieur de Noirmont then went to his wife and said to her in a cold and impressive tone:
- 70. “Your humor isvery capricious, madame, as anyone may see by the way in which you treat your daughter sometimes; but you extend it to defenceless servants also, and that is what I cannot endure. This young Louise, who came here to wait upon Ernestine, is honest and virtuous; her appearance is as becoming as her manners; I think that it would be difficult to find another so satisfactory; and yet you propose to dismiss her, madame —you expect me to turn a good girl out of my house, because, for some unknown reason, she has ceased to please you; because your fanciful humor makes you more difficult than ever to serve!—No, madame, that shall not be; I propose to be just before everything, and this girl shall remain in my house, because it would be unjust to send her away.” Madame de Noirmont had not a word to say in reply; she hung her head and seemed completely crushed.
- 71. PART IV XXIV THE POLISHINTRIGUE Chérubin did not see Daréna for a week; he fretted and fumed with impatience, fearing that his intrigue with the pretty Pole had fallen through altogether; and, as is always the case, he became immeasurably more enamored of the object of his passion as his fear of not possessing her increased. It was for the purpose of giving him time to reach that climax of passion, that Daréna, who was thoroughly acquainted with the human heart, had allowed several days to elapse without going to see him. At last Daréna appeared at the hôtel de Grandvilain one morning, hurried and breathless, like a man who had galloped twelve leagues without a halt. He pushed old Jasmin aside and almost knocked him down, when that worthy retainer attempted to tell him that he did not know whether he could see his master, who had not yet risen. “I don’t care whether he’s up or in bed, he is always visible to me,” replied Daréna imperiously. “Learn, you old donkey of a valet, to know the persons whom your master is always delighted to receive.” As he spoke, Daréna rushed into the young marquis’s bedroom, leaving Jasmin propped against the wall, muttering in a voice that trembled with wrath: “Old donkey! he called me an old donkey! He’s an impertinent knave. The Grandvilains, father or son, never called me that. He’s not a donkey, but I have an idea that he’s a much more dangerous animal!” Daréna reached Chérubin’s bedside and pulled the curtains aside, crying: “Up, Joconde! up, Lovelace, Richelieu, Rochester! The moment of triumph has arrived at last!—Sapristi! I can fairly say, my dear fellow, that I have made myself ill for you! Ouf! I can do no more!”
- 72. And Daréna threwhimself on a couch, and mopped his face with his handkerchief. “But what has become of you during these eight long days that I have not once seen you, and have not known what to think of your silence?” asked Chérubin, looking closely at his friend. “I thought that you had forgotten me.” “Ah! that is just like a man—a young man! Because things are not done on the instant, you think that you are forgotten. Do I ever forget my friends? Am I not absolutely devoted to you? If you have not heard from me for a week, it is because I had nothing to tell you; but I have been on the lookout, watching and waiting for the moment to act. It has come at last; I have acted, and the fair Globeska is in our power.” “Is it possible? Oh! do tell me how you did it, my dear Daréna?” “Parbleu! by my ordinary method: I scattered money about. I know no other way, especially as it always succeeds. Dress, and meanwhile I will tell you how it all came about; but don’t call your valet; you will understand that I can’t talk about it before a witness. I have already compromised myself enough—but damn the odds!” Chérubin rose and began to dress, saying: “Go on, I am listening; I shall not lose a word.” “You know that the pretty Pole lived with her husband in furnished lodgings in the Marais; I succeeded in effecting the delivery of your billet- doux by bribing a lady’s maid and two concierges. The Comtesse de Globeska replied that she was mad over you and asked nothing better than to leave her tyrant. That was all very well, but how were we to abduct the young woman from a man who left her no more than her shadow? It was very difficult. Seven days passed thus; Monsieur de Globeski did not leave his wife for an instant. At last, yesterday, I learned from a concierge, by a further use of money, that the Polish count had decided to leave Paris, and that he was going to take his wife to Norway; of course, if we had had to pursue our conquest to Norway, it would have taken us too far. I instantly formed my resolution, saying to myself: ‘He shall not take her!’ “I learned—still by the lavish use of money—that the post-chaise was to call for our Poles at eight in the evening. I arrived just before the hour; the carriage came and stopped in front of the house, and I went boldly up to the postilion and led him aside.
- 73. “‘I adore thewoman who is going with you,’ I said. ‘I am going to follow with two friends to a lonely place on the road, one or two leagues from Paris; we shall pretend to attack you, and fire a few shots with pistols loaded with powder only. You will stop; we will open the carriage door and seize the young woman; then you will start off at full speed with the old gentleman, and if he shouts to you to stop, you will pay no attention until you have galloped at least two solid hours.’ “You will understand, my dear Chérubin, that I should not dare to make such a proposition as that to a postilion, without supporting it by convincing arguments. I handed him a thousand-franc note, and he turned his back, saying: “‘What do you take me for?’ “I added five hundred francs. He remarked that it was a very ticklish business! I added another five hundred. He agreed to everything. That’s the way things are done in Paris. I went off to choose two rascals on whom I could rely, in consideration of five hundred francs, which I gave to each. I also hired a post-chaise. When the Comte de Globeski started off with his wife, we followed; and, about two leagues from here, between Sèvres and Chaville, in a place where nothing grows but melons, we discharged our pistols. The bribed postilion stopped. It was dark, and everything went off as I had arranged. We kidnapped the young woman. The old Pole defended her like a genuine demon; indeed, he inflicted a slight dagger wound on one of our men in the scuffle, which forced me to disburse three hundred francs more. However, we captured the divine Globeska, and I took her to the house I have hired, where she passed the night and is now awaiting you.” “Oh! what a series of events, my dear Daréna! But great heaven! this stealing a woman from her husband, and by force! Suppose it should be known? Isn’t it a crime?” “Bah! are you going to have scruples now?—At all events, there was no other way, and then, if worse comes to worst, I am the only one compromised; but my friendship is of the sort that defies danger.” “And the pretty Pole—where have you taken her?” “To a little house that stands all by itself near Barrière de la Chopinette; I could find nothing better. And then I considered that to go into the country, at a distance from Paris, would incommode you too much. The house I have hired is in a spot where very few people pass; the outlook is not very
- 74. cheerful, but whatdo you care for that? You aren’t going to shut yourself up with a woman, to look out of the windows at people passing, are you? Isn’t one always happy when with the person one loves?” “Oh, yes! of course; but in what quarter is this Barrière de la Chopinette?” “In the quarter of La Poudrette, and of lonely promenades, in the direction of Ménilmontant. However, we can go there in a cab. Remember, my dear fellow, that your charmer is waiting for you; I told the concierge of the house to order as toothsome a breakfast as he can procure in that quarter, and some superfine wines. Make haste and finish dressing—put on your best clothes, perfume yourself——” “Perfume myself? Indeed, I shall not; perfumery makes me sick.” “As you please, but put on your armor. Lucky Chérubin! you are about to possess one of the loveliest women I have ever seen; and her Polish accent, too, is most fascinating.” “And she loves me, you say? she has admitted it?” “Parbleu! how many times must I tell you? In fact, I should say that her conduct was quite sufficient proof of it.” “She didn’t weep when she was kidnapped?” “Weep! She danced—she adores dancing, it seems. By the way, I need not tell you that I have nothing left of the funds you advanced me. The postilion and my men to pay—the hire of the post-chaise and the house— and all the people I bribed. In fact, you owe me fifteen hundred francs.” “Fifteen hundred francs!” exclaimed Chérubin, as he walked to his desk; “it costs a lot to abduct a woman!” “To whom are you telling that? to me, who have abducted a hundred perhaps, in the course of my life? Indeed it was in that way that I spent a large part of my fortune; but it is a princely pleasure all the same, in which everybody cannot indulge.” Chérubin handed Daréna the sum that he required, and said: “I am ready.” “Very good; send out for a cab; you will understand that we can’t go to your petite maison with your tilbury and your groom. You should never take your servants into the secret of a mysterious intrigue like this; such people are too fond of talking.”
- 75. “You are right.—Holà!Jasmin!” The old servant appeared, still with a long face, and cast an angry glance at Daréna. Chérubin ordered him to send for a cab. “Will not monsieur take his cabriolet?” queried Jasmin, with an expression of surprise. “Evidently not!” cried Daréna, laughing at Jasmin’s face; “as your master orders a cab, he doesn’t propose to take his cabriolet. Off with you, old ruin, and make haste, if you possibly can.” “Old ruin!” muttered Jasmin, as he left the room. “Still another insult— and I must swallow it all! I am very much afraid that this ne’er-do-well will ruin my young master. I should like to know why he makes him take a cab, when he has his own tilbury and cabriolet.” However, Jasmin did his errand; the cab was summoned. Chérubin went downstairs with Daréna, and they both entered the vehicle, which Jasmin looked after, with a far from pleased expression, as it drove away. Daréna told the driver where to take them. After quite a long drive they stopped in front of a shabby house outside Barrière de la Chopinette, on the outer boulevards. “Here we are!” said Daréna, jumping out of the cab. Chérubin looked at the house, which had but one floor above the ground floor, with two windows on the front. “This isn’t a very handsome house!” he exclaimed. “It is very fine inside,” replied Daréna. “The principal thing is that it’s isolated; the devil himself would be in it if the husband should unearth you here! My dear fellow, when you run off with a woman, you must take the greatest precautions. And after all, what do you care about the house? It’s the woman that you come here to see. For my part, I should have been perfectly happy in a shepherd’s hut, with the object of my love.—Send the cab away; I am going to ring.” Chérubin made haste to pay the cab-driver, who returned to his box and drove away. Daréna pulled a wire beside the low door that gave admission to the house. A little fellow of some thirteen years, with an impudent expression, whose knavish and insolent bearing harmonized well with a very dirty costume, answered the bell, his cap over his ear, his blouse flapping in the
- 76. wind, and hishands black with dirt. He bestowed a glance of intelligence on Daréna, who recognized little Bruno, the same urchin of whom Poterne had tried to make a monkey, and who, on his side, had conceived the idea of appropriating the skin which he had used in studying his character. Later Poterne had found Bruno, who had squandered his disguise; the business agent took the liberty of thrashing the boy, then forgave him, and charmed by the happy talents which young Bruno manifested, determined to employ him again when the opportunity should present itself. In the scheme which had been devised to dupe Chérubin, it was necessary to station some intelligent person, who could be trusted, in the house which had been hired. Poterne instantly thought of the urchin, to whom he did not pay much, and who had all the qualities essential to forward their designs. “Ah! this is the concierge’s son,” said Daréna, glancing at Bruno as they entered the house, and leading Chérubin through a sort of vestibule, toward the staircase. “Where’s your father, my boy? is he away?” “Yes, monsieur, he had to go to a place ten leagues from here, to see my aunt, who is very sick.” “And you are keeping the house?” “Yes, monsieur.” “Has the lady who slept here had everything that she wanted?” “Oh, yes! monsieur; don’t you be afraid; that lady hasn’t wanted for anything. She’s upstairs. By the way, she says that she’s beginning to get tired of being all alone.” “Patience! monsieur here has come to keep her company.—How about the breakfast; is it ordered?” “Yes, monsieur; and it will be fine, I tell you. I was the one that went to the restaurant——” “This little rascal is overflowing with intelligence,” said Daréna, turning to Chérubin, “and I recommend him to you in case you need anything.— Well, my dear friend, here you are with your charmer now, and I will leave you.” “What! you are going to leave me?” cried Chérubin, almost in an offended tone. “Why, I don’t see that there is anything more for me to do here; the rest is your business. You are going to breakfast tête-à-tête with a little
- 77. foreigner, who ismad over you. Would not a third person be in the way?” “Oh, yes! of course. Well, then, au revoir.” “Au revoir, my dear marquis, and may love crown you with its sweetest favors!” Daréna smiled, almost ironically, as he shook hands with Chérubin; then he flashed a glance at Bruno and left the house, closing the door behind him. Chérubin felt intensely excited when he found himself in that strange house, in a quarter which was entirely unfamiliar to him, with no other company than a boy who stared at him with a sly expression, as he cracked nut after nut which he took from under his blouse. The vestibule had two doors, both of which were open, disclosing the interior of two rooms, in one of which the only furniture was several rickety tables, and in the other, one table and a wretched cot bed; the windows on the boulevard were supplied with iron bars, but entirely unprovided with curtains. Chérubin, who had seen this at a glance, reflected that Daréna had not spent much money in furnishing the house. Then he turned to Bruno, who was still breaking nuts, sometimes with his teeth and sometimes with his feet, and humming at intervals a tune of which nothing could be heard save: tu tu tu tu tu tu r’lu tu. “Where is madame la comtesse’s apartment?” “Whose?” queried the ex-bootblack, looking up with an insolent expression. “I ask you where the young lady is, who has been in this house since last night?” The boy thrust his tongue into his cheek,—a street Arab’s trick when he proposes to lie—and answered: “Oh, yes; the young foreign lady, who was kidnapped, and who slept here—tu tu tu r’lu tu—she’s upstairs, on the first floor, in the finest apartment in the house, where she’s sighing and having a stupid time—tu tu tu r’lu tu!” Chérubin asked no further questions; he went upstairs—there was but one flight—and stopped at a door, the key of which was on the outside. His heart beat very fast at the thought that he was about to stand in the presence
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