The document outlines Arnab Sinha's Ph.D. research work on fast texture synthesis algorithms based on non-parametric Markov random field (NMRF) models. The research aims to address problems with existing NMRF texture synthesis algorithms related to high computational complexity. Key contributions include developing new methods for order estimation from the Fourier domain, reducing dimensionality to lower computational complexity, revisiting order estimation, and inverse texture synthesis. Future work may explore additional dimensionality reduction techniques and faster neighborhood search methods.
Uniform and non uniform single image deblurring based on sparse representatio...ijma
Considering the sparseness property of images, a sparse representation based iterative deblurring method
is presented for single image deblurring under uniform and non-uniform motion blur. The approach taken
is based on sparse and redundant representations over adaptively training dictionaries from single
blurred-noisy image itself. Further, the K-SVD algorithm is used to obtain a dictionary that describes the
image contents effectively. Comprehensive experimental evaluation demonstrate that the proposed
framework integrating the sparseness property of images, adaptive dictionary training and iterative
deblurring scheme together significantly improves the deblurring performance and is comparable with the
state-of-the art deblurring algorithms and seeks a powerful solution to an ill-conditioned inverse problem.
Neural Network Based Noise Identification in Digital ImagesIDES Editor
Image noise is unwanted information in an image
and can occur at any moment of time such as during image
capture, transmission, or processing and it may or may not
depend on image content. In order to remove the noise from
the noisy image, prior knowledge about the nature of noise
must be known otherwise noise removal causes the image
blurring. Identifying nature of noise is a challenging problem.
Many researchers have proposed their ideas on image noise
identification and each of the work has its assumptions,
advantages and limitations. In this paper, we proposed a new
methodology based on neural network for identifying the
different types of noise such as Non Gaussian, Gaussian white,
Salt and Pepper and Speckle noise.
Removing noise from the Medical image is still a challenging problem for researchers. Noise added is not easy to remove from the images. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper summarizes the major techniques to denoise the medical images and finds the one is better for image denoising. We can conclude that the Multiwavelet technique with Soft threshold is the best technique for image denoising.
Image Splicing Detection involving Moment-based Feature Extraction and Classi...IDES Editor
In the modern age, the digital image has taken
the place of the original analog photograph, and the forgery
of digital images has become increasingly easy, and harder
to detect. Image splicing is the process of making a
composite picture by cutting and joining two or more
photographs. An approach to efficient image splicing
detection is proposed here. The spliced image often
introduces a number of sharp transitions such as lines,
edges and corners. Phase congruency is a sensitive measure
of these sharp transitions and is hence proposed as a
feature for splicing detection. Statistical moments of
characteristic functions of wavelet sub-bands have been
examined to detect the differences between the authentic
images and spliced images. Image splicing detection can be
treated as a two-class pattern recognition problem, which
builds the model using moment features and some other
parameters extracted from the given test image. Artificial
neural network (ANN) is chosen as a classifier to train and
test the given images.
Uniform and non uniform single image deblurring based on sparse representatio...ijma
Considering the sparseness property of images, a sparse representation based iterative deblurring method
is presented for single image deblurring under uniform and non-uniform motion blur. The approach taken
is based on sparse and redundant representations over adaptively training dictionaries from single
blurred-noisy image itself. Further, the K-SVD algorithm is used to obtain a dictionary that describes the
image contents effectively. Comprehensive experimental evaluation demonstrate that the proposed
framework integrating the sparseness property of images, adaptive dictionary training and iterative
deblurring scheme together significantly improves the deblurring performance and is comparable with the
state-of-the art deblurring algorithms and seeks a powerful solution to an ill-conditioned inverse problem.
Neural Network Based Noise Identification in Digital ImagesIDES Editor
Image noise is unwanted information in an image
and can occur at any moment of time such as during image
capture, transmission, or processing and it may or may not
depend on image content. In order to remove the noise from
the noisy image, prior knowledge about the nature of noise
must be known otherwise noise removal causes the image
blurring. Identifying nature of noise is a challenging problem.
Many researchers have proposed their ideas on image noise
identification and each of the work has its assumptions,
advantages and limitations. In this paper, we proposed a new
methodology based on neural network for identifying the
different types of noise such as Non Gaussian, Gaussian white,
Salt and Pepper and Speckle noise.
Removing noise from the Medical image is still a challenging problem for researchers. Noise added is not easy to remove from the images. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper summarizes the major techniques to denoise the medical images and finds the one is better for image denoising. We can conclude that the Multiwavelet technique with Soft threshold is the best technique for image denoising.
Image Splicing Detection involving Moment-based Feature Extraction and Classi...IDES Editor
In the modern age, the digital image has taken
the place of the original analog photograph, and the forgery
of digital images has become increasingly easy, and harder
to detect. Image splicing is the process of making a
composite picture by cutting and joining two or more
photographs. An approach to efficient image splicing
detection is proposed here. The spliced image often
introduces a number of sharp transitions such as lines,
edges and corners. Phase congruency is a sensitive measure
of these sharp transitions and is hence proposed as a
feature for splicing detection. Statistical moments of
characteristic functions of wavelet sub-bands have been
examined to detect the differences between the authentic
images and spliced images. Image splicing detection can be
treated as a two-class pattern recognition problem, which
builds the model using moment features and some other
parameters extracted from the given test image. Artificial
neural network (ANN) is chosen as a classifier to train and
test the given images.
Adaptive Neuro-Fuzzy Inference System based Fractal Image CompressionIDES Editor
This paper presents an Adaptive Neuro-Fuzzy
Inference System (ANFIS) model for fractal image
compression. One of the image compression techniques in
the spatial domain is Fractal Image Compression (FIC)
but the main drawback of FIC using traditional
exhaustive search is that it involves more computational
time due to global search. In order to improve the
computational time and compression ratio, artificial
intelligence technique like ANFIS has been used. Feature
extraction reduces the dimensionality of the problem and
enables the ANFIS network to be trained on an image
separate from the test image thus reducing the
computational time. Lowering the dimensionality of the
problem reduces the computations required during the
search. The main advantage of ANFIS network is that it
can adapt itself from the training data and produce a
fuzzy inference system. The network adapts itself
according to the distribution of feature space observed
during training. Computer simulations reveal that the
network has been properly trained and the fuzzy system
thus evolved, classifies the domains correctly with
minimum deviation which helps in encoding the image
using FIC.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The objective of this work is to propose an image
denoising technique and compare it with image denoising
using ridgelets. The proposed method uses slantlet transform
instead of wavelets in ridgelet transform. Experimental result
shows that the proposed method is more effective than ridgelets
in noise removal. The proposed method is effective in
compressing images while preserving edges.
Despeckling of Ultrasound Imaging using Median Regularized Coupled PdeIDES Editor
This paper presents an approach for reducing speckle
in ultrasound images using Coupled Partial Differential
Equation (CPDE) which has been obtained by uniting secondorder
and the fourth-order partial differential equations. Using
PDE to reduce the speckle is the noise-smoothing methods
which is getting attention widely, because PDE can keep the
edge well when it reduces the noise. We also introduced a
median regulator to guide energy source to boost the features
in the image and regularize the diffusion. The proposed
method is tested in both simulated and real medical
ultrasound images. The proposed method is compared with
SRAD, Perona Malik diffusion and Non linear coherent
diffusion methods, our method gives better result in terms of
CNR, SSIM and FOM.
Blur Parameter Identification using Support Vector MachineIDES Editor
This paper presents a scheme to identify the blur
parameters using support vector machine (SVM) Multiclass
approach has been used to classify the length of motion blur
and sigma parameter of atmospheric blur. Different models
of SVM have been constructed to classify the parameters.
Experimental results show the robustness of the proposed
approach to classify blur parameters.
Q-filter Structures for Advancing Pattern Recognition SystemsMagdi Mohamed
An advanced approach for adaptive nonlinear digital data processing is described in this presentation. Three primal computational structures referred to as Q-Measures, Q-Metrics, and Q-Aggregates are introduced and utilized in unison as highly adaptive data analysis handlers. The proposed approach relies on universal functionals using few parameters to characterize dynamic system behaviors in broad ranges of unconventional measure, metric, and aggregation spaces. We present this unique approach in application to real-valued signal processing tasks, with suitable optimization algorithms, so that the parameters of the proposed models can be tuned automatically. The new approach is tested on real data sets to enable applications in mobile communication systems and the experiments show promising results.
Denoising and Edge Detection Using SobelmethodIJMER
The main aim of our study is to detect edges in the image without any noise , In many of the images edges carry important information of the image, this paper presents a method which consists of sobel operator and discrete wavelet de-noising to do edge detection on images which include white Gaussian noises. There were so many methods for the edge detection, sobel is the one of the method, by using this sobel operator or median filtering, salt and pepper noise cannot be removed properly, so firstly we use complex wavelet to remove noise and sobel operator is used to do edge detection on the image. Through the pictures obtained by the experiment, we can observe that compared to other methods, the method has more obvious effect on edge detection.
Adaptive Neuro-Fuzzy Inference System based Fractal Image CompressionIDES Editor
This paper presents an Adaptive Neuro-Fuzzy
Inference System (ANFIS) model for fractal image
compression. One of the image compression techniques in
the spatial domain is Fractal Image Compression (FIC)
but the main drawback of FIC using traditional
exhaustive search is that it involves more computational
time due to global search. In order to improve the
computational time and compression ratio, artificial
intelligence technique like ANFIS has been used. Feature
extraction reduces the dimensionality of the problem and
enables the ANFIS network to be trained on an image
separate from the test image thus reducing the
computational time. Lowering the dimensionality of the
problem reduces the computations required during the
search. The main advantage of ANFIS network is that it
can adapt itself from the training data and produce a
fuzzy inference system. The network adapts itself
according to the distribution of feature space observed
during training. Computer simulations reveal that the
network has been properly trained and the fuzzy system
thus evolved, classifies the domains correctly with
minimum deviation which helps in encoding the image
using FIC.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The objective of this work is to propose an image
denoising technique and compare it with image denoising
using ridgelets. The proposed method uses slantlet transform
instead of wavelets in ridgelet transform. Experimental result
shows that the proposed method is more effective than ridgelets
in noise removal. The proposed method is effective in
compressing images while preserving edges.
Despeckling of Ultrasound Imaging using Median Regularized Coupled PdeIDES Editor
This paper presents an approach for reducing speckle
in ultrasound images using Coupled Partial Differential
Equation (CPDE) which has been obtained by uniting secondorder
and the fourth-order partial differential equations. Using
PDE to reduce the speckle is the noise-smoothing methods
which is getting attention widely, because PDE can keep the
edge well when it reduces the noise. We also introduced a
median regulator to guide energy source to boost the features
in the image and regularize the diffusion. The proposed
method is tested in both simulated and real medical
ultrasound images. The proposed method is compared with
SRAD, Perona Malik diffusion and Non linear coherent
diffusion methods, our method gives better result in terms of
CNR, SSIM and FOM.
Blur Parameter Identification using Support Vector MachineIDES Editor
This paper presents a scheme to identify the blur
parameters using support vector machine (SVM) Multiclass
approach has been used to classify the length of motion blur
and sigma parameter of atmospheric blur. Different models
of SVM have been constructed to classify the parameters.
Experimental results show the robustness of the proposed
approach to classify blur parameters.
Q-filter Structures for Advancing Pattern Recognition SystemsMagdi Mohamed
An advanced approach for adaptive nonlinear digital data processing is described in this presentation. Three primal computational structures referred to as Q-Measures, Q-Metrics, and Q-Aggregates are introduced and utilized in unison as highly adaptive data analysis handlers. The proposed approach relies on universal functionals using few parameters to characterize dynamic system behaviors in broad ranges of unconventional measure, metric, and aggregation spaces. We present this unique approach in application to real-valued signal processing tasks, with suitable optimization algorithms, so that the parameters of the proposed models can be tuned automatically. The new approach is tested on real data sets to enable applications in mobile communication systems and the experiments show promising results.
Denoising and Edge Detection Using SobelmethodIJMER
The main aim of our study is to detect edges in the image without any noise , In many of the images edges carry important information of the image, this paper presents a method which consists of sobel operator and discrete wavelet de-noising to do edge detection on images which include white Gaussian noises. There were so many methods for the edge detection, sobel is the one of the method, by using this sobel operator or median filtering, salt and pepper noise cannot be removed properly, so firstly we use complex wavelet to remove noise and sobel operator is used to do edge detection on the image. Through the pictures obtained by the experiment, we can observe that compared to other methods, the method has more obvious effect on edge detection.
Modern Periodic Law,Classification of Elements, Periodicity in Atomic Properties,Atomic Radius, Ionisation potential or Ionisation Energy,Electron Affinity
Active Strokes: Coherent Line Stylization for Animated 3D ModelsPierre Bénard
These slides presents a method for creating coherently animated line drawings that include strong abstraction and stylization effects. These effects are achieved with active strokes: 2D contours that approximate and track the lines of an animated 3D scene. Active strokes perform two functions: they connect and smooth unorganized line samples, and they carry coherent parameterization to support stylized rendering. Line samples are approximated and tracked using active contours ("snakes") that automatically update their arrangment and topology to match the animation. Parameterization is maintained by brush paths that follow the snakes but are independent, permitting substantial shape abstraction without compromising fidelity in tracking. This approach renders complex models in a wide range of styles at interactive rates, making it suitable for applications like games and interactive illustrations.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Delivering Micro-Credentials in Technical and Vocational Education and TrainingAG2 Design
Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
For more detailed information on delivering micro-credentials in TVET, visit this https://tvettrainer.com/delivering-micro-credentials-in-tvet/
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Computationally Efficient NMRF model based Texture Synthesis
1. Outline
Ph.D. Research Work
Conclusion and Possible Future Directions
Fast NMRF based texture synthesis algorithms
Arnab Sinha
arnab@iitk.ac.in
April 16, 2009
Thesis Supervisor: Dr. Sumana Gupta
ACES-205, Dept. of EE, Indian Institute of Technology Kanpur, India
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
2. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
1 Outline
Earlier Methods
Research problems in NMRF-tex-syn algorithms
2 Ph.D. Research Work
Order Estimation from Fourier Domain
Reduction of Computational complexity
Order Estimation : Revisited
Inverse Texture Synthesis
3 Conclusion and Possible Future Directions
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
3. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
The significance of texture synthesis
• What defines texture ?
• Locally varying intensities and/or color values
• The local variations can be found perceptually similar within the total region
• Texture Synthesis:
Original D104 Texture
Given a small texture exempler, synthesize
an arbitrary sample of texture, so that the
synthesized texture is visually similar to the
original sample.
Synthesized texture should look alike the original texture
• Application of texture synthesis in -
• Image segmentation, classification, synthesis, etc.
• Content-based image retrieval
• Development of high-level computer vision algorithms
• Animation of real scenes
• Perceptual analysis
• Computationally fast and efficient handling of objects
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
4. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Texture synthesis: Difficulty
Figure: Spectrum of Natural Textures
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
5. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Brief History of Models
Texture Synthesis Algorithm
Image Domain Model Mixed Domain Model Transformed Domain Model
Non−Linear Models
Linear Non−Linear
Hidden Markov Tree Non−Linearity Introduced
by Histogram Equalization
Fan and Xia (2003)
2D−NCAR, Hard−limited Gaussian
Process
Chellappa and Kashyap (1985)
Jacovitti et al. (1998)
2D−Wold
Francos et al. (1993) Zhang et al. (1998)
Wavelet + AR
2D− MA
1. Zhu et al. (1997)
Eom (1998) Circular Harmonic Func 2. Zhu et al. (2000)
+ Hard−limited Gaussian
Campasi and Scarano (2002)
3. Portilla and Simoncelli (2000)
NNMRF
Charalampidis (2006)
Paget and Longstaff (1998)
Mathematical Models
Intuitive Models
Heeger and Bergen (1995)
Efros and Leung (1999)
Wei and Levoy (2000)
Pixel−based Ashikhmin (2001) We are working
within this
Framework
Sampling Process
Tonietto et al. (2005)
Kwatra et al. (2003)
Patch−based
Patch−based sampling with wavelet transformation
Wu et al. (2004) as a feature set for graph−cut algorithm
Popular Methods
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
6. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Description of N-MRF model
• S is the lattice
• Ys is the random variable at site s ∈ S
• Concept of Neighborhood system:
ℵs
•s
s = (i,j), site
• r ∈ ℵs ⇔ s ∈ ℵr
1st order neighbors
2 2
• Circular neighborhood: ℵs = {r; s.t., |r − s| ≤ o } { } 2nd order neighbors
• say, Xs = {Yr ; r ∈ ℵs }
• Say, Y(s) = {Yr ; r s}, r, s ∈ S
• Definition of MRF: P(Ys |Y(s) ) = P(Ys |{Yr ; r ∈ ℵs })
• parameteric model for P(Ys |Xs )
• semi-parameteric model for P(Ys |Xs )
• non-parameteric model for P(Ys |Xs )
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
7. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Description of N-MRF model: Kernel Density Estimation
Definition of KDE, [Scott(1992)]
N
1
• single dimensional: P(x) = N Kh (x − xi )
i=1
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
8. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Description of N-MRF model: Kernel Density Estimation
Definition of KDE, [Scott(1992)]
N
1
• single dimensional: P(x) = N Kh (x − xi )
i=1
N d
1
• multi-dimensional: P(X) = Khj (X (j) − Xi (j))
i=1 j=1
N
(X (j)−Xi (j))2
• where, in case of Gaussian kernel, Khj (X (j) − Xi (j)) = √1 }
exp{−
2hj2
N 2πhj
• and, hj = σj N −1/(d+4)
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
9. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Texture Synthesis Algorithm
Some definitions
• Input texture field: {Ys }, where, s ∈ Sin
• Output texture field: {Yq }, where, q ∈ Sout
Kh (Ys −Yq )Kh (Xs −Xq )
s∈Sin Y X
• Definition of LCPDF: P(Yq |Xq ) =
Kh (Xs −Xq )
s∈Sin X
Iterative Conditional Mode (ICM) algorithm
• Evaluate P(Yq = y|Xq ), for y = 0, 1, . . . , 255 gray values.
• Assign Yq = y, for which the above conditional probability is maximum
Local Simulated Annealing
• Define a Confidence field, Cq ; q ∈ Sout , and a matrix Φq = DIAG{Cr ; r ∈ ℵq }
• KhX (Xs − Xq ; Φq ) = exp{−(Xs − Xq )T Φh,q (Xs − Xq )}, and Φh,q = Φq HX ≈ hΦq
• Updation rule for the confidence field
1
• Cq = min{1, |r∈ℵ | r∈ℵ Cr + u × e}
q
q
• where, u is a random number and e is a constant scale factor
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
10. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Texture Synthesis Algorithm
Approximate Independent Conditional Mode (ICM) algorithm
• Ds,q = (Xs − Xq )T Φq (Xs − Xq )
• Define Sq = {r ∈ Sin } ⊂ Sin , s.t., ∀r ∈ Sq , Dr,q = constant.
• Assign Yq = yr , where r is sampled from the set Sq randomly.
S in
S out C
q q
Input texture
Output Texture Confidence Field
Output Neighborhood Output Confidence
Vector X q Vector Wq
Matrix
Input Neighborhood Vectors Similarity Measure
t
{X s} N−MRF : ( X q − X s) ( X q − X s)
t
WL alg : ( X q − X s) ( X q − X s)
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
11. Outline
Earlier Methods
Ph.D. Research Work
Research problems in NMRF-tex-syn algorithms
Conclusion and Possible Future Directions
Research Problems
• Order estimation
• Large Computational Complexity
• Computational complexity ∝ d, the dimension of the neighborhood vector.
• Computational complexity ∝ (M × N), the input image size
• Computational complexity ∝ I, the number of iterations required to attain global
convergence
Original Texture
Neighborhood vector dimension ’d’
8000
7000
computational complexity of
6000
texture synthesis algorithm
is proportional to ’d’
5000
4000
3000
2000
1000
0
0 10 20 30 40 50
Model order ’o’
Order 4 Order 8 Order 14
Figure: Effect of order on the synthesis results and computational complexity
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
12. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Order estimation from two fundamental frequencies
Y
c
d
o
b
a X
Yj
Xj
Yi
Xi
Figure: Points a, b, c, d are the four corners of texton defined by the fundamental spatial period
vectors [Xi Yi ] and [Xj Yj ]. The major diagonal o gives the order of causal circular neighborhood
and o/2 gives the order of non-causal circular neighborhood.
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
13. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Extraction of the parameters
• Dimitri’s algorithm
• estimate the two fundamental frequecies from the two-dimensional DFT of the texture
sample.
• computational complexity is of the order of image size.
• Hays’s algorithm
• it estimates the two fundamental spatial vectors from the correlation function
• the algorithm is iterative
• computationally expensive with respect to Dimitri’s algorithm
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
14. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
D21
D20
order = 9
order = 23 order = 4
order = 18
D52
D35
order = 48 order = 8 order = 22
order = 21
Figure: Comparison of estimated order through Dimitrios and Hays’s methods with (NR) texture
synthesis results
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
15. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
A new neighborhood system
Y
proposed Non−causal
neighborhood
X
Yj
Xj
Yi
circular Non−causal
neighborhood
Xi
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
16. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results: Proposed neighborhood system
Circular Neighborhood Proposed Neighborhood Proposed Neighborhood
Circular Neighborhood
D104
D65
D95
D64
D67
D3
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
17. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Two approaches
Computational complexity affected by
the neighbourhood dimension, d, and
1
the number of input pixels, N
2
Reduction methodologies
Dimensionality reduction methodologies, e.g., Principal Component Analysis
1
(PCA) – to reduce the effect of d
A data structure for fast search
2
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
18. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
With Dimensionality reduction methods
How the distance metric Ds,q looks after projection
(Xq − Xs )T Φq (Xq − Xs ) (X q − X s )T Φ q (X q − X s )
≈
[PrT Pr (Xq − Xs )]T Φq [PrT Pr (Xq − Xs )]
=
[Pr (Xq − Xs )]T Pr Φq PrT [Pr (Xq − Xs )]
=
(Zq − Zs )T Ψq (Zq − Zs )
=
T
• What is Ψq = Pr Φq Pr ?
• Is it reducing the computational complexity ?
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
19. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Simulated Annealing for Principal components
Original Ds,q
(Xq − Xs )T Φq (Xq − Xs )
=
Ds,q
where, Φq = DIAG{W1 , W2 , . . . , Wd }
ˆ
Proposed Ds,q
ˆ ˆ
(Zq − Zs )T Φq (Zq − Zs )
=
Ds,q
ˆ
where, Φq = DIAG{W1 , W2 , . . . , Wk }
WHY ? Because we need only
• a steady increase in the value of confidence, and
• the starting value has to be ”0” and ending value has to be ”1”
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
20. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results
Table: Comparison of dimensionality; Original dimension, |ℵs | = d; Reduced dimension, k (<< d), η
is the ratio of computational complexities between earlier and proposed one
Texture Type Texture order d k η
NR D20 20 1516 60 21.9405
NR D3 30 2820 580 3.7926
NR D21 25 1960 56 29.2642
NR D22 20 1256 177 6.3042
NR D35 28 2452 287 6.6612
NR D36 22 1516 258 5.1024
ST D7 27 2288 511 3.6438
ST D13 24 1792 131 11.6006
NR+ST D18 32 3208 95 25.5666
NR+ST D4 29 2628 465 4.4755
NR+ST D5 29 2628 179 11.6262
IN/STR D15 23 1652 167 8.4897
IN/STR D42 26 2120 293 5.9699
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
21. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results continued ...
NNMRF Proposed Algorithm Proposed Algorithm
NNMRF
D20 D7
k = 511
d = 2288
d = 1516 k=60
D13
D21
k=131
d=1792
d=1960 k=56
D22 D42
k = 293
d=2120
k = 177
d=1256
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
22. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
With Fast Kernel Density Estimation
Assumption: The h parameters along all the directions are equal.
• Let Rn = {ts : ||ts − tn || ≤ R}
N
1
• P(tn ) = N s=1 KH (ts − tn )
Y
1
• P(tn ) = N s∈Rn KH (ts − tn )
• Let Nn = |{s Rn }|
R=100
1
= KH (ts − tn )
Err(tn , R)
N
s Rn
Nn
K (R)
≤
To calculate KDE
NH
at this target point
X we only need
KH (R)
≤
Source data vector these two points
Target data vector
max(Err)
• Rel err(R) =
max(Probability)
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
23. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Earlier FKDE algorithms
• Improved Fast Gaussian Transform (IFGT)
[Yang et al.(2003)Yang, Duraiswami, Gumerov, and Davis]
• kd-tree based FKDE [Gray and Moore(2003)]
• Reconstructionhistogram [Zhang et al.(2005)Zhang, Tang, and Kwok]
Reconstructionhistogram
• Clustering: {Clusti ; i = 1 . . . M}
• Let ni as the number of source data vectors within i th cluster
M
1
• P(tn ) = N i=1 KH (tn − Clusti )ni
• KDE of tn given the source data points at cluster centroids with a weight factor
ni /N
• flexibility ?
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
24. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Improved Fast Gaussian Transform
• P(tn ) = KH (tn − Clusti )f (tn , Clusti )
||tn −Clusti ||≤RIFGT
1
• P(tn ) = N KH (tn − ts )
||tn −Clusti ||≤RIFGT s∈Clusti
Source data clusters
Target data
vectors
Due to
this overlap
we need to
consider this
source cluster
R IFGT R
To consider the source cluster
In effect it can include some source cluster
R
the radius threshold has to be IFGT
which was not needed at all
The R IFGT can vary with the overlap size
and cluster shape
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
25. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
kd-tree-based FKDE
Build up the kd-tree and Search according to the radius R.
Y
6
σ X > σY
Hyper−Sphere
Y
-6 -
Partition
Span in Y direction
e
6 e
ee
R max_rec_err
Hyper−Rectangle
e ee e
e
e e
e
e
e
Eigen vectors
e
e
e e e
e
e
e
Centroid
e
e
-
e ee
Sub-spaces
e
e
-
e
?
e
X
e
Reconstruction
X Error R rec_err,n
-
R
tn
> R+ R max_rec_err
-
?
Span in X direction
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
26. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Why do we need another algorithm for FKDE
Table: Why do we need another algorithm for FKDE ?
C-FKDE KD-FKDE
Advantage Clustering algorithm provides more Due to the hyper-plane boundary,
one can use original radius R
compact representation of the data
space for strict error bound
optimal RIFGT has to estimated
Disadvantage kd-tree is not a good clustering
for every tn , maximum RIFGT algorithm, therefore it does not
can increase computational provide compact representation
complexity of the data space
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
27. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Principal Directive Divisive Partitioning (PDDP)[Boley(1998)]
• project each source data point within the present space onto the first principal
direction (eigen vector corresponding to the largest eigen value).
• partition the present space into two sub-spaces with respect to the mean (or
median) of the projected values.
Hieararchical Boundaries
Source data
Tree structure of the nodes
6th
IV I
1st
VI 7th
2nd II III
I
III
II VII
5th V VI VII
4th IV
8th
V 8th
6th 7th
2nd 3rd 4th 5th
1st
3rd
Leaf nodes
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
28. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
FKDE based on PDDP
If the present node is a leaf then evaluate KDE.
1
Source data vectors
Projection of source data
Target data vector
(t n) Projection of terget point
D rec_err
2nd Direction T is within left child
D If R D rec_err
T
Return 0
Drec_err Else
If D R process both children
Process its children D
2nd Direction
Dlb
(Boundary for Partition)
1st Direction
mr
vn D
For the right child lb
If Dlb R
(Which child to process)
(Process child) Return 0
If Dlb R = return 0 if D R = process left child Else If R D rec_err
Else if Drec_err R = return 0 Else process both children Return 0
Else process Else
Process its children
vn Projected target data vector
mr Projected mean vector 1st Direction
(a) Target point is outside (b) Target point is inside
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
29. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
FKDE based on PDDP
If the present node is a leaf then evaluate KDE.
1
Is there any need to go further for the children of the present node ?
2
Source data vectors
Projection of source data
Target data vector
(t n) Projection of terget point
D rec_err
2nd Direction T is within left child
D If R D rec_err
T
Return 0
Drec_err Else
If D R process both children
Process its children D
2nd Direction
Dlb
(Boundary for Partition)
1st Direction
mr
vn D
For the right child lb
If Dlb R
(Which child to process)
(Process child) Return 0
If Dlb R = return 0 if D R = process left child Else If R D rec_err
Else if Drec_err R = return 0 Else process both children Return 0
Else process Else
Process its children
vn Projected target data vector
mr Projected mean vector 1st Direction
(c) Target point is outside (d) Target point is inside
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
30. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
FKDE based on PDDP
If the present node is a leaf then evaluate KDE.
1
Is there any need to go further for the children of the present node ?
2
Which child node (left or right or both) of the present node to process further ?
3
Source data vectors
Projection of source data
Target data vector
(t n) Projection of terget point
D rec_err
2nd Direction T is within left child
D If R D rec_err
T
Return 0
Drec_err Else
If D R process both children
Process its children D
2nd Direction
Dlb
(Boundary for Partition)
1st Direction
mr
vn D
For the right child lb
If Dlb R
(Which child to process)
(Process child) Return 0
If Dlb R = return 0 if D R = process left child Else If R D rec_err
Else if Drec_err R = return 0 Else process both children Return 0
Else process Else
Process its children
vn Projected target data vector
mr Projected mean vector 1st Direction
(e) Target point is outside (f) Target point is inside
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
31. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Comparison between the FKDE algorithms
(i−1,j)
2
(i,j+1)
3
(i,j) 1
4
(i,j+1)
{1} X RGB == 3 dimensions
{1,2} X RGB == 6 dimensions
{1,2,3} X RGB == 9 dimensions
{1,2,3,4} X RGB == 12 dimensions
(g) Image considered (h) Creation of the data
for creating the data set space
Figure: Data set creation for FKDE analysis
Table: Time comparison
Dimension 3 6 9 12
KDE: Time (sec) 981.78 1204.77 2529.22 2668.58
PDDP-FKDE: Time (sec) 11.3 23.39 52.55 65.79
KD-FKDE: Time (sec) 22.55 33.88 110.62 228.44
IFGT-FKDE: Time (sec) 399.79 425.45 209.33 384.08
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
33. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Computationally efficient Texture synthesis algorithm with FKDE
algorithms
Problems
how to include the effect of Wq (the temperature field) within the PDDP-based tree
1
structure for the implementation of FKDE, and
there are two joint densities corresponding to {Yq , Xq } and Xq ; therefore, it
2
requires two FKDE structure, which is not computationally efficient.
Inclusion of Wq
• Starting State:
{Wq,i = 0} ⇒ P(Xq ; Wq ) = constant
⇒ P(Xq ) is uniform
⇒ Each Xs has equal effect upon Xq
⇒ Every Xs should be considered in the KDE
⇒ Rnew is very large
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
34. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Computationally efficient Texture synthesis algorithm with FKDE
algorithms
Problems
how to include the effect of Wq (the temperature field) within the PDDP-based tree
1
structure for the implementation of FKDE, and
there are two joint densities corresponding to {Yq , Xq } and Xq ; therefore, it
2
requires two FKDE structure, which is not computationally efficient.
Inclusion of Wq
• Starting State:
{Wq,i = 0} ⇒ P(Xq ; Wq ) = constant
⇒ P(Xq ) is uniform
⇒ Each Xs has equal effect upon Xq
⇒ Every Xs should be considered in the KDE
⇒ Rnew is very large
• Ending State:
{Wq,i = 1} ⇒ P(Xq ; Wq ) = P(Xq )
⇒ Rnew = R
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
35. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Computationally efficient Texture synthesis algorithm with FKDE
algorithms
Problems
how to include the effect of Wq (the temperature field) within the PDDP-based tree
1
structure for the implementation of FKDE, and
there are two joint densities corresponding to {Yq , Xq } and Xq ; therefore, it
2
requires two FKDE structure, which is not computationally efficient.
Inclusion of Wq
• Starting State:
{Wq,i = 0} ⇒ P(Xq ; Wq ) = constant R
=
Rnew
⇒ P(Xq ) is uniform cq
⇒ Each Xs has equal effect upon Xq
abs(vn − mr ) ≤ Rnew
⇒ Every Xs should be considered in the KDE
R
⇒ Rnew is very large ⇒ abs(vn − mr ) ≤
cq
• Ending State:
⇒ abs(vn − mr )cq ≤ R
{Wq,i = 1} ⇒ P(Xq ; Wq ) = P(Xq )
⇒ Rnew = R
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
36. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results with comparisons
Original NNMRF kd−tree
IFGT Proposed
D102
D49
D20
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
37. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results with comparisons
Original kd−tree
NNMRF IFGT Proposed
D53
D104
D4
D82
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
38. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results with comparisons
Original NNMRF IFGT kd−tree Proposed
D110
D60
D93
D97
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
39. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results with comparisons
Table: Time taken in texture synthesis: input texture size 128 × 128 and output texture size
256 × 256
NNMRF C-FKDE KD-FKDE PDDP-FKDE
hours 8 5 8 6
minutes 7 55 34 0
seconds 39 12 56 41
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
40. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Maximum Log-Pseudo-likelihood
LPL = log[P(Ys |Xs )]
s∈Sin
For 1st order neighborhood system For 2nd order neighborhood system
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
41. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
How to estimate MLPL ?
• parametric MRF model
• non-parametric MRF model: what should be the kernel ?
• Gaussian kernel: as used in [Paget and Longstaff(1998)]
• Dirac-delta kernel
• Some other solution
Effect of kernel upon the MLPL estimate
nd
LPL is getting saturated before 2 order
LPL is not saturating rather it is increasing
0
−10000
−50
−20000
−100
−30000 −150
−40000
LPL
−200
LPL
−250
−50000
D102: Near regular
−300
D104: Near regular
−60000
−350
D110: Stochastic
−70000 −400
D60: Stochastic
D93: Stochastic −450
−80000
0 1 2 3 4
0 5 10 15 20 25 30 35 40
Order
Order
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
42. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Why does the original LPL measure, not saturate ?
Why ?
Kh (Ys −Yq )Kh (Xs −Xq )
s∈S
• original LCPDF: p(Yq |Xq ) =
q∈S Kh (Xs −Xq )
• Changing terms with order:
• hy = σy N −1/(d+4) : changes due to change in d and N, with order
√
• In case of LCPDF the normalizing term becomes: 2πhy ;
• Moreover, hy also affect the argument within the exponential term.
• One can not neglect this term.
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
43. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
A new definition for LCPDF
δ(Ys − Yq )Kh (Xs − Xq )
q∈S
p(Ys |Xs ) =
Kh (Xs − Xq )
q∈S
Two reasons in the support for this new definition
• From the texture synthesis algorithm point of view
• From a numerical point of view
0.018
0.016
Probability calculated with Gaussian kernel
D104 Near Regular Texture
0.014
D110 Stochastic Texture
0.012
0.01
probaility = 0.003544
0.008
0.006 Probability = 0.0002963
0.004
0.002
0
0 50 100 150 200 250 300
Gray Levels
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
44. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results: D104
D104
8
2 6
4
10 14
12 16
22 24
18 20
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
45. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results: D9
D9
5
1 3 7
9 11 13 15
19
17 21 23
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
46. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results for Near-regular textures
Original Original NNMRF Our Synthesis Algorithm
NNMRF Our Synthesis Algorithm
D104 D20
o = 12 o = 18
D22 D34
o = 17
0 = 13
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
47. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results for Stochastic textures
Our Synthesis Algorithm
Original NNMRF Original NNMRF
Our Synthesis Algorithm
D4 D9
O=9
O = 10
D93 D97
O = 16
O=9
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
48. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Results for Some other textures
Original NNMRF Our Synthesis Algorithm Original NNMRF Our Synthesis Algorithm
D53 D55
O = 14
O = 17
D82
D80
O = 14 O = 12
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
49. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Problem Definition
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
50. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Problem Definition
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
51. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Problem Definition
Texture synthesis
HOW ?
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
52. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Motivation
Applications of Inverse Texture Synthesis
• Understanding of Textures
• Content-based image/video retrieval
• Perceptual Image/Video compression
• Computer Vision Tasks
• Perceptual understanding of textures within the image
• Creation of animation – Collecting information from natural images/sequences
• Perceptual Understanding of temporal texture – such as, dance sequence, walk
sequence, music sequence etc.
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
53. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Definition of Objective Functions
According to N-MRF model
• Distance between two LCPDF’s evaluated w.r.t. both input and output texture
patches.
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
54. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Definition of Objective Functions
According to N-MRF model
• Distance between two LCPDF’s evaluated w.r.t. both input and output texture
patches.
• What distance function ?
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
55. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Definition of Objective Functions
According to N-MRF model
• Distance between two LCPDF’s evaluated w.r.t. both input and output texture
patches.
• What distance function ?
• Computationally expensive
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
56. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Definition of Objective Functions
According to N-MRF model
• Distance between two LCPDF’s evaluated w.r.t. both input and output texture
patches.
• What distance function ?
• Computationally expensive
According to N-MRF model: Intuitively
• M×N
• Size of the output patch
1
min{||Xs − Xq ||2 , where
• |S |
• Do the input neighborhood vectors s∈Sin
in
exist within output patch ? q ∈ Sout }
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
57. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Problem with these two objective functions
Scaled up versions of solutions
A B
approximately
same
Neighborhood
Deformation/variation within quot;Aquot;
difficult to find within quot;Bquot;
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
58. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Three objectives
• Say Sout = {s ∈ Sin , s.t., (si − i)2 ≤ M 2 and (sj − j)2 ≤ N 2 }
{i,j,M,N}
= S − Sout
• Define S
in
• First objective finds neighborhood from input texture within the output texture
• Second objective finds neighborhood from output texture within the input texture,
excluding the part of Sout
1
min{||Xs − Xq ||2 ; q ∈ Sout }
=
F1
|Sin |
s∈Sin
1 {i,j,M,N}
min{||Xq − Xs ||2 ; s ∈ Sin
= }
F2
|Sout |
q∈Sout
= M×N
F3
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
59. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Multi-objective Framework
f1 (x)
f2 (x)
inequality constraints: gj (x) ≥ 0, j = 1, 2, ..., J
such that
minx .
equality constraints: hk (x) = 0, k = 1, 2, ..., K
.
.
solution space: xiL ≤xi ≤ xiU , i = 1, 2, ..., N
fm (x)
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
60. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Multi-objective Framework
f1 (x)
f2 (x)
inequality constraints: gj (x) ≥ 0, j = 1, 2, ..., J
such that
minx .
equality constraints: hk (x) = 0, k = 1, 2, ..., K
.
.
solution space: xiL ≤xi ≤ xiU , i = 1, 2, ..., N
fm (x)
Domination
A vector x ∈ RN is said to dominate y ∈ RN if both the conditions stated below hold
true:
fi (x) ≤ fi (y), ∀i ∈ [1 . . . m]
∃ j ∈ [1 . . . m], such that, fj (x) fj (y)
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms
61. Order Estimation from Fourier Domain
Outline
Reduction of Computational complexity
Ph.D. Research Work
Order Estimation : Revisited
Conclusion and Possible Future Directions
Inverse Texture Synthesis
Pareto-optimal Front
Best in F 1
2nd objective function F 2
Worst in F 2
All are optimal
solutions Best in F 2
Worst in F 1
1st objective function F1
Arnab Sinha arnab@iitk.ac.in Fast NMRF based texture synthesis algorithms