The document presents a novel image compression technique using contourlet transform and adaptive multistage vector quantization, specifically aimed at compressing retinal and fingerprint images. It highlights the importance of effective compression for storage of high-resolution images in medical diagnostics and security. Results indicate that this method achieves improved compression ratios and higher peak signal-to-noise ratios compared to traditional wavelet methods.

1. International journal of Computer Networking and Communication (IJCNAC)Vol. 1, No. 2(November 2013)
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EFFICIENT IMAGE COMPRESSION USING
LAPLACIAN PYRAMIDAL FILTERS FOR
EDGE IMAGES
V.Karthikeyan1 and V.J.Vijayalakshmi2
1
Department of ECE, SVS College of Engineering, Coimbatore, India
Karthick77keyan@gmail.com
2
Department of EEE, Sri Krishna College of Engg & Tech., Coimbatore, India
Vijik810@gmail.com
Abstract
This project presents a new image compression technique for the coding of retinal and
fingerprint images. Retinal images are used to detect diseases like diabetes or
hypertension. Fingerprint images are used for the security purpose. In this work, the
contourlet transform of the retinal and fingerprint image is taken first. The coefficients of
the contourlet transform are quantized using adaptive multistage vector quantization
scheme. The number of code vectors in the adaptive vector quantization scheme depends
on the dynamic range of the input image.
Keywords: Counterlet Transform, adaptive multistage vector quantization,
hypertension, Fingerprint image
1. INTRODUCTION
The retina is the only location where blood vessels can be visualized non-invasively in vivo.
The evaluation of retinal images is a diagnostic tool widely used to gather information about
patient retinopathy. Diabetic retinopathy is the leading cause of blindness in the adult population.
Mass screening efforts are necessary to detect diabetic retinopathy. Traditionally the retina has
been observed either directly through an ophthalmoscope or fundus camera. But high resolution
retinal images are necessary to in order to identify features such as exudates and micro
aneurysms. High resolution image in turn occupy large storage space. In order to store thousands
of records of patients, effective retinal image compression is necessary. The Contour let
transform has better performance in representing edges than wavelets for its anisotropy and
directionality; hence it is well suited for multi-scale image representation. The Contourlet
coefficients in the corresponding sub bands are quantized using adaptive multi-stage vector
quantization. Vector quantization (VQ) has been proven a powerful compression scheme for
coding of images and image sequences. The applicability of VQ is, however, limited by an
exponential growth of the computational complexity with the vector dimension. For this reason,
low dimensionality VQ are typically used in image compression, but such VQ limit the coding
efficiency and tend to yield highly visible block boundaries in low bit rate applications.
Multistage Vector Quantization (MSVQ) is a structured VQ scheme in which the search time and
codebook complexity reduction with respect to optimal VQ is obtainable. Compression is
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performed by a program that uses a formula or algorithm to determine how to compress or
decompress data. Graphic image file formats are usually designed to compress information as
much as possible (since these can tend to become very large files). Graphic image compression
can be either lossy (some information is permanently lost) or lossless (all information can be
restored).
Compressing an image is significantly different than compressing raw binary data. This also
means that lossy compression techniques can be used in this area. The present study is envisaged
to improve the image coding method by using the contourlet transform. The Contourlet transform
has better performance in representing edges than wavelets for its anisotropy and directionality;
hence it is well suited for multi-scale image representation. The Contourlet coefficient has less
computational complexity with the vector dimension. For this reason, low dimensionality VQ is
typically used in image compression, but such the corresponding sub-bands are quantized using
adaptive multi-stage vector quantization. Vector quantization (VQ) has been proven a powerful
compression scheme for coding of images and image sequences. Multistage Vector Quantization
(MSVQ) is a structured VQ scheme in which the search time and codebook complexity reduction
with respect to optimal VQ is obtainable.
1.1. Error Metrics
Two of the error metrics used to compare the various image compression techniques are the Mean
Square Error (MSE) and the Peak Signal to Noise Ratio (PSNR). The MSE is the cumulative
squared error between the compressed and the original image, whereas PSNR is a measure of the
peak error. The mathematical formulae for the two are
MSE =
(1)
PSNR = 20 * log10 (255 / sqrt (MSE))
(2)
Where I(x, y) is the original image, I'(x, y) is the approximated version (which is actually the
decompressed image) and M, N are the dimensions of the images. A lower value for MSE means
lesser error, and as seen from the inverse relation between the MSE and PSNR, this translates to a
high value of PSNR. Logically, a higher value of PSNR is good because it means that the ratio of
Signal to Noise is higher. Here, the 'signal' is the original image, and the 'noise' is the error in
reconstruction. So, if you find a compression scheme having a lower MSE (and a high PSNR),
you can recognize that it is a better one.
2.
PROPOSED COMPRESSION METHOD
In this project, we propose an image compression scheme using successive approximation
quantization of vectors of the contourlet transformed image for edge images like fundus image,
retinal image. The Contourlet Transform is a directional transform, which is capable of capturing
contours and fine details in images. The pyramidal directional filter bank (PDFB), was proposed
by MinhDo and Vetterli, which overcomes the block-based approach of curvelet transform by a
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3. International journal of Computer Networking and Communication (IJCNAC)Vol. 1, No. 2(November 2013)
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directional filter bank, applied on the whole scale also known as contour let transform (CT). In
essence, first a wavelet-like transform is used for edge (points) detection, and then a local
directional transform for contour segments detection. With this insight, one can construct a
double filter bank structure in which at first the Laplacian pyramid (LP) is used to capture the
point discontinuities, and followed by a directional filter bank (DFB) to link point discontinuities
into linear structures. The overall result is an image expansion with basis images as contour
segments, and thus it is named the contourlet transform. The combination of this double filter
bank is named pyramidal directional filter bank (PDFB).
The flow graph of the contourlet transform is depicted in below Fig. The LP decomposition at
each level generates a down sampled low pass version of the original and the difference between
the original and the prediction, resulting in a band pass image. Band pass images from the LP are
fed into a DFB so that directional information can be captured. The DFB is efficiently
implemented through an I-level binary tree decomposition that leads to 2/ sub bands with wedgeshaped frequency partitioning as illustrated below. The cascading of LP and DFB results in
Pyramidal Directional Filter Bank (PDFB). In this contour let scheme, each generation doubles
the spatial resolution as well as the angular resolution. The PDFB provides a frame expansion for
images with frame elements like contour segments, and thus is also called the contourlet
transform.
2.1. Laplacian Pyramid
One way of achieving a multiscale decomposition is to use a Laplacian pyramid (LP),
introduced by Burt and Adelson. The LP decomposition at each level generates a down sampled
lowpass version of the original and the difference between the original and the prediction,
resulting in a bandpass image as shown in Fig. In this figure, ‘H’ and ‘G’ are called analysis and
synthesis filters and ‘M’ is the sampling matrix. The process can be iterated on the coarse version.
In Fig. the outputs are a coarse approximation ‘a’ and a difference ‘b’ between the original signal
and the prediction. The original image is convolved with a Gaussian kernel. The resulting image
is a low pass filtered version of the original image.
Fig.1. Laplacian pyramid scheme (a) analysis, and (b) reconstruction.
Thus the Laplacian pyramid is a set of band pass filters. By repeating these steps several times a
sequence of images, are obtained. If these images are stacked one above another, the result is a
tapering pyramid data structure, as shown in Fig. and hence the name.
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2.2.
Directional Filter Bank
In 1992, Bamberger and Smith introduced a 2-D directional filter bank (DFB) that can be
maximally decimated while achieving perfect reconstruction. The directional filter bank is a
critically sampled filter bank that can decompose images into any power of two’s number of
directions. The DFB is efficiently implemented via an l-level tree structured decomposition that
leads to ‘2l’ sub bands with wedge-shaped frequency partition as shown in Fig. The original
construction of the DFB involves modulating the input signal and using diamond shaped filters.
Therefore, the LP permits further sub band decomposition to be applied on its band pass images.
Those band pass images can be fed into a DFB so that directional information can be captured
efficiently. The scheme can be iterated repeatedly on the coarse image. The end result is a double
iterated filter bank structure, named pyramidal directional filter bank (PDFB), which decomposes
images into directional sub bands at multiple scales. The scheme is flexible since it allows for a
different number of directions at each scale.
Fig.2. Laplacian pyramid structure.
3.
MULTISTAGE VECTOR QUANTIZATION
In vector quantization, an input vector of signal samples is quantized by selecting the best
matching representation from a codebook of ‘2kr’ stored code vectors of dimension k. VQ is an
optimal coding technique in the sense that all other methods of coding a random vector in ‘k’
dimensions with a specific number b=kr of bits are equivalent to special cases of VQ with
generally suboptimal codebooks.
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Fig.3. Multistage Vector Quantization Scheme
The resulting encoding and storage complexity, of the order of 2kr, may be prohibitive
for many applications. A structured VQ scheme which can achieve very low encoding
and storage complexity is multistage VQ (MSVQ). In MSVQ, the kr bits are divided
between L stages with bi bits for stage ‘i’. The storage complexity of MSVQ is
as
vectors, which can be much less than the complexity
of vectors for
unstructured VQ. MSVQ is a sequential quantization operation where each stage
quantizes the residual of the previous stage.
The structure of MSVQ encoder consists of a cascade of VQ stages as shown in Fig. 9.
For an Lstage MSVQ, an l th –stage quantizer l Q, l =0, 1, 2…L −1 is associated with a
stage codebook l C contains l K stage code vectors. The set of stage quantizes
are equivalent to a single quantizerQ, which is referred to as the
direct sum vector quantizer.
4. ADAPTIVE VECTOR QUANTIZATION
In this paper, we have proposed an adaptive vector quantizer which is based on the
dynamic range of the input image. A vector quantizer is defined as a mapping 'Q' of 'L'
dimensional Euclidean space into a finite subset Y which is given by
Q:
RL=Y
Where 'V' is the set of reproduction vectors, which is generally termed as VQ codebook
Y = (xi; i =1, 2, N). Here x represents the code vectors and 'N' is the number of vectors in
the code book 'V'. The first step in the proposed adaptive vector quantization scheme is to
split the image into a set of 'L' dimensions. Two important factors which decide the size
of the code book are rate (R) and dimension (L). The number of code vectors in the code
book is 2RL
• In our algorithm, the dynamic range of the input image is determined first. The dynamic
range is given by
Dynamic range = Maximum gray level value – Minimum gray level value.
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This dynamic range is used to fix the interval of the vector space to be partitioned. The
interval is calculated as
In our approach, the general expression of code vector for L=2 is given by
(3)
Where i, j are integers (i, j = 0, 1, 2.). Successive vectors are formed by adding the interval in
both dimensions to the initial code vector. After forming the code vectors, the next step is to
project the input vector into the code vector. Each input vector is matched with a closest
codeword in the codebook, and then the index of the codeword is transmitted instead of the code
vector itself the matching of the input vector to the nearest code vector is based on minimum
distortion. A distortion measured is used to assign the cost of reproducing any vector as
reproduction. A quantizer is optimal if it minimizes the average distortion. The squared error
distortion is
(4)
The multistage vector quantization scheme is shown in Fig. 4. In the figure, 'X' represents
the input vector, LUT stands for Look up table, i1, i2 represents the indices from different
stages.
Fig.4.Block Diagram of the Proposed System
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7. International journal of Computer Networking and Communication (IJCNAC)Vol. 1, No. 2(November 2013)
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PROPOSED ALGORITHM
The proposed retinal image coder scheme is summarized below
•
•
•
The correlation present in the input retinal image is minimized by taking the
contourlet transform of the input retinal image. Different pyramidal and
directional filters are taken into consideration in this work.
The transform coefficients obtained in step 1 are adaptively vector quantized in a
multistage manner where the residual coefficients due to quantization are
iteratively feedback and vector quantized. The number of code vectors depends on
the dynamic range of the input image; hence it is adaptive in nature.
The output indices from step 2 are lossless coded using static Huffman code. In
decoding, the decoder basically performs the reverse process of the above steps.
The different pyramidal filters taken into consideration are 'Haar', 'biorthogonal
9/7'. The different directional filters taken into consideration are 'pkva' and
'biorthogonal 9/7'. In the case of wavelets, the different wavelet filters chosen are
'Haar', 'biorthogonal 9/7' and 'la8'. Table 1 shows the performance of the proposed
algorithm for the first, second and third level of decomposition by varying the bits per
dimension (bpd) from 0.125 to 1.0. From the table it is obvious that in the case of contour
lets, as the level of decomposition increases, the Peak Signal to Noise Ratio (PSNR)
value slightly increases
6. SIMULATION OUTPUTS
In this project work we proposed a new retinal and fingerprint image compression
scheme using successive approximation quantization of vectors of the contourlet
transformed image. In this a new image compression scheme using successive
approximation quantization of the image using Laplacian filter with noise variance of
about γ = 0.01 and we have to prove that we preserve the meta information like edges.
So we also take edge images as a data base. Here we may achieve even upto 1:80
compression ratio with PSNR around 30 db.
(a)
(b)
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(c)
Fig.5. (a) Input image (b).Contour Coefficient Level 1 (c) the compressed image using the
contourlet transforms
6.
CONCLUSION
From the experimental results, it can be observed that for the same bits per dimension, the PSNR
obtained using contourlet transform is better than that of the wavelet transform. Hence, a better
image reconstruction is possible with less number of bits using contourlet transform. In retinal
images, the optic nerves are having higher amount of contoured patterns hence contourlet
performs superior than wavelet. Higher PSNR results can be obtained by including more number
of stages in multi-stage vector quantization, which will result in increased computational
complexity.
REFERENCES
[1]
M.N. Do and M. Vetterli, "The contourlet transform: an efficient directional multiresolution image
representation," IEEE Trans. of Image Processing, vol. 14, no. 12, pp. 2091-2106, December
2004.
[2]
A. Gersho and R. Gray, Vector Quantization and Signal Compression, Kluwer Academic
Publishers, M.A., 1995.
[3]
R.M. Gray, "Vector Quantization," IEEE ASSP magazine, vol. 1, no. 2, pp. 4 - 29, Apr. 1984.
[4]
M.N. Do, Directional multiresolution image representations, Ph.D. thesis, EPFL, Lausanne,
Switzerland, Dec. 2001.
[5]
P. J. Burt and E.H. Adelson, "The Laplacian pyramid as a compact image code," IEEE Trans.
Commun, vol. 31, pp. 532-540, Apr. 1983.
[6]
R. H. Bamberger and M. 1. T Smith, "A filter bank for the directional decomposition of images:
Theory and design," IEEE Trans. Signal Proc. vol. 40, pp. 882-893, Apr. 1992.
[7]
R.C.Gonzalez, R.E.Woods, Digital Image Processing, New Delhi, Pearson Education Pvt. Ltd.,
2nd Edition.
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[8]
Khalid Sayood, Introduction to Data Compression, New Delhi, Harcourt India Private Limited,
2nd edition, 2000.
[9]
Vivien Chappelier, Christine de Beaulieu, “Image Coding with Iterated Contourlet and Wavelet
Transforms”, IEEE International Conference on Image Processing (ICIP 2004),
Vol. 5, pp. 3157-3160, Oct. 2004.
[10]
Ramin Eslami, Hayder Radha, “Wavelet-Based Contourlet Transform and its Application to
Image Coding”, IEEE International Conference on Image Processing (ICIP 2004), Vol. 5, pp.
3189-3192, Oct. 2004.
Authors
Prof.V.Karthikeyan has received his Bachelor’s Degree in Electronics and
Communication Engineering from PGP college of Engineering and Technology in
2003, Namakkal, India, He received Masters Degree in Applied Electronics from KSR
college of Technology, Erode in 2006 He is currently working as Assistant Professor in
SVS College of Engineering and Technology, Coimbatore. He has about 8 years of
Teaching Experience
Prof.V.J.Vijayalakshmi has completed her Bachelor’s Degree in Electrical &
Electronics Engineering from Sri Ramakrishna Engineering College, Coimbatore,
India. She finished her Masters Degree in Power Systems Engineering from Anna
University of Technology, Coimbatore, She is currently working as Assistant Professor
in Sri Krishna College of Engineering and Technology, Coimbatore She has about 5
years of teaching Experience.
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