Introduction to Nonlinear Image Processing
|
|
|
- Christine Scott
- 6 years ago
- Views:
Transcription
1 Introduction to Nonlinear Image Processing 1 IPAM Summer School on Computer Vision July 22, 2013 Iasonas Kokkinos Center for Visual Computing Ecole Centrale Paris / INRIA Saclay
2 Mean and median 2 Observations in a 3x3 window: Mean: ( )/9 = 13.1 Median: 1) Sort: 2) Pick mid-point robust to outliers non-linear outlier [1, 2, 100, 1, 3, 2, 1, 5, 3] [1, 1, 1, 2, 2, 3, 3, 5, 100] "
3 Mean 3
4 Median 4
5 Gaussian blur 5
6 Image Processing 6 f!! (f) image filter image Previous lecture: ( f + h) = (f)+ (h) This lecture: remove this constraint freedom! at the expense of control
7 Multi-scale Gaussian smoothing g (x, y) = exp x 2 + y =5 = 10 = 20
8 Gaussian scale space Rewrite Gaussian: g t (x, y) = 1 4 t exp x 2 + y 2 4t t = time Scale space: u(x, y, t) =g t (x, y) u 0 (x, y), t > 0 u(x, y, 0) = u 0 (x, y) A. Witkin, Scale-space filtering, IJCAI, J. Koenderink, The structure of images, Biological Cybernetics, 1984 J. Babaud, A. P. Witkin, M. Baudin, and R. O. Duda, Uniqueness of the Gaussian kernel for scale-space filtering, PAMI, A. Yuille, T.A. Poggio: Scaling theorems for zero crossings. PAMI, T. Lindeberg, Scale-Space Theory in Computer Vision, Kluwer, 1994 L. Florack, Image Structure, Kluwer, 1997 B. Romeny, Front-End Vision and Multi-Scale Image Analysis, Kluwer, J. Weickert, Linear scale space has first been proposed in Japan. JMIV, 1999.
9 Heat diffusion and image processing 9 Gaussian satisfies: Scale-space satisfies: Associative property: u(x, y, t) =g t (x, y) u 0 (x, y) f [g h] =[f u(x, y, 0) = u 0 (x, y) Heat diffusion PDE (Partial Differential Equation)
10 Heat diffusion and image processing 10
11 Heat diffusion in 1D u t = u xx = d dx d dx u 11
12 Heat diffusion in 1D inhomogeneous material u t = d dx conductivity c d dx u 12 12
13 Heat diffusion in 2D 13 Homogeneous material u x! ru =(u x,u y ) d dx u x! Inhomogeneous material d dx (cu x)! div(cru) u t =div(cru) u u y u t = u xx + u yy
14 Perona-Malik Diffusion 14 Image-dependent conductivity u t =div(g ( ru ) ru) s 2 g(s) =exp a 2 u(x, y, 0) = u 0 (x, y) Diffusion stops at strong image gradients (structure-preserving) CLMC formulation: ru! rg u P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, PAMI 1990 F. Catte, P.L. Lions, J.M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Analysis, 1992
15 Nonlinear vs. linear diffusion 15 (a) Linear diffusion at t=2 (b) Nonlinear diffusion at t=4.4
16 Extension to vectorial images 16 Extension of nonlinear diffusion to vectorial images: generalization where:
17 Nonlinear diffusion for color image denoising 17 (a) Color Image with Noise (b) Perona-Malik diffusion
18 Variational interpretation of heat diffusion 18 Cost functional: Euler-Lagrange: Heat diffusion: modifies temperature to decrease E quickly
19 Variational techniques 19 Denoising as functional minimization Functional: encodes undesirable properties Total Variation: u 1 (x) u 2 (x) TV[u 1 ] = TV[u 2 ] Minimization flow TV[f] = TV[g] = TV[h] w 1 (x) w 2 (x) Rudin, L. I.; Osher, S.; Fatemi, E. "Nonlinear total variation based noise removal algorithms". Physica D 60, 1992 TV[w 1 ] > TV[w 2 ]
20 Total Variation diffusion 20 (a) Noisy image (b) Total Variation diffusion
21 Perona-Malik versus Total Variation 21 (a) Perona-Malik diffusion s 2 g(s) =exp K 2 (b) Total-Variation diffusion g(s) = 1 s
22 What is the right cost functional? 22 Can we learn the cost function? S.C. Zhu, Y. N. Wu and D. Mumford, FRAME, IJCV 1997 Filters: Use Gabors, Difference-of-Gaussians, Gaussian filters, Random Fields: Construct distribution that reproduces their histograms And Maximum Entropy: while being as random as possible Natural images: natural image statistics Training: Sample:
23 From FRAME to GRADE 23 Ø Ø GRADE: Gibbs Reaction & Diffusion Equation GRADE: maximize image probability using Euler-Largange PDEs S.C. Zhu, Y. N. Wu, D. Mumford, Filters, Random Fields and Max. Ent., IJCV S.C. Zhu and D. Mumford, Gibbs Reaction and Diffusion Equation, PAMI S. Roth and M. Black, Fields of Experts, IJCV 2009
24 Second Moment Matrix 24 Distribution of gradients: J = apple P x 0,y 0 Ix 2 P x 0,y 0 I x I y Px P 0,y 0 I x I y x 0,y 0 I 2 y
25 Second Moment Matrix 25 Distribution of gradients: J = X x 0,y 0 (I x,i y ) T (I x,i y )
26 Second Moment Matrix 26 Distribution of gradients: J = X x 0,y 0 (rg u) T (rg u)
27 Second Moment Matrix 27 Distribution of gradients: J = G h i (rg u) T (rg u)
28 Second Moment Matrix 28 J = G h i (rg u) T (rg u) Eigenvectors : directions of maximal and minimal variation of u Eigenvalues: amounts of minimal and maximal variation u
29 Anisotropic diffusion structure tensor 29 Nonlinear diffusion u t =div(g ( ru ) ru) Nonlinear Anisotropic diffusion diffusion tensor u t =div(t (J (ru ) ru) Slide credit: A. Roussos J. Weickert, Coherence-Enhancing Diffusion Filtering, Image and Vision Computing, R. Kimmel, R. Malladi, and N. Sochen. Images as Embedded Maps and Minimal Surfaces, IJCV, D. Tschumperlé, and R. Deriche (2005), Vector-valued image regularization with PDE s. PAMI, A. Roussos and P. Maragos, Reversible Interpolation of vectorial Images, IJCV 2009 M. Lindenbaum, M. Fischer and A. Bruckstein, "On Gabor's contribution to image enhancement, D. Gabor, Information theory in electron microscopy, 1965
30 Anisotropic Diffusion example 30 Slide credits: A. Roussos
31 Anisotropic Diffusion example 31 Slide credits: A. Roussos
32 Nonlinear anisotropic diffusion 32 Extension to vectorial images Structure tensor for vectorial image: Slide credits: A. Roussos
33 Nonlinear anisotropic diffusion 33 Noisy input Nonlinear Anisotropic Diffusion Slide credits: A. Roussos
34 Nonlinear vs. Nonlinear and anisotropic diffusion 34 Nonlinear Diffusion Nonlinear Anisotropic Diffusion Slide credits: A. Roussos
35 Nonlinear vs. Nonlinear and anisotropic diffusion 35 Nonlinear Diffusion Nonlinear Anisotropic Diffusion Slide credits: A. Roussos
36 Inpainting problem 36 Inpainting region D (a) Image with missing region (b) Initial prediction (constant) (c1) 300 iterations (c2) 600 iterations (c3) 1500 iterations (converged) M. Bertalmío, G. Sapiro, V. Caselles and C. Ballester., "Image Inpainting", SIGGRAPH 200 T. F. Chan and J. Shen, "Mathematical Models for Local Nontexture Inpainting", SIAM, 200
37 Application: text removal 37 (a) Input (b) Total Variation Inainting Slide credits: A. Roussos
38 Application: fake bravado 38 Slide credits: A. Roussos
39 PDE-based interpolation Interpolation problem 39 (a) Low resolution input image (b) Zero-Padding initialization (c) 4x4 PDE-based magnification A. Roussos and P. Maragos, Reversible Interpolation of vectorial Images, IJCV 2009
40 PDE-based interpolation 40 (a) Input Signal (b) Bicubic interpolation (4 x 4) (d) PDE-based interpolation(4 x 4) A. Roussos and P. Maragos, Reversible Interpolation of vectorial Images, IJCV 2009
41 PDE-based interpolation 41 (a) Low-resolution Input (b) Initialization: Zero-Padding (c) 4x4 PDE-based interpolation A. Roussos and P. Maragos, Reversible Interpolation of vectorial Images, IJCV 2009
42 PDE-based interpolation 42 (a) Input (b) Bilinear Interpolation (c) TV based Interpolation (d) Structure-tensor based interpolation A. Roussos and P. Maragos, Reversible Interpolation of vectorial Images, IJCV 2009
43 Further study 43 Fast numerical solutions G. Papandreou and P. Maragos, Multigrid Geometric Active Contour Models,TIP, J. Weickert and B. H. Romeny, 'Efficient Schemes for Nonlinear Diffusion Filtering', TIP '98 A. Chambolle, 'An Algorithm for Total Variation Minimization and Applications', JMIV 2004 T. Goldstein, S. Osher The Split Bregman method for L1-regularized problems, SIAM 2009 Not covered in this talk Bilteral Filter, Non-Local Means Buades, B. Coll, and J. Morel, A non-local algorithm for image denoising, CVPR, 2005 C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, ICCV 1998 P Milanfar, " A Tour of Modern Image Filtering ", IEEE Signal Processing Magazine, 2013 Online software
Tensor-based Image Diffusions Derived from Generalizations of the Total Variation and Beltrami Functionals
Generalizations of the Total Variation and Beltrami Functionals 29 September 2010 International Conference on Image Processing 2010, Hong Kong Anastasios Roussos and Petros Maragos Computer Vision, Speech
Nonlinear diffusion filtering on extended neighborhood
Applied Numerical Mathematics 5 005) 1 11 www.elsevier.com/locate/apnum Nonlinear diffusion filtering on extended neighborhood Danny Barash Genome Diversity Center, Institute of Evolution, University of
Introduction to motion correspondence
Introduction to motion correspondence 1 IPAM - UCLA July 24, 2013 Iasonas Kokkinos Center for Visual Computing Ecole Centrale Paris / INRIA Saclay Why estimate visual motion? 2 Tracking Segmentation Structure
R. Kimmel, 1 R. Malladi, 1 and N. Sochen 2. Lawrence Berkeley National Laboratory University of California, Berkeley,
Image Processing via the Beltrami Operator? R. Kimmel, 1 R. Malladi, 1 and N. Sochen 2 1 Lawrence Berkeley National Laboratory University of California, Berkeley, CA 94720. 2 Electrical Engineering Dept.
Efficient Beltrami Filtering of Color Images via Vector Extrapolation
Efficient Beltrami Filtering of Color Images via Vector Extrapolation Lorina Dascal, Guy Rosman, and Ron Kimmel Computer Science Department, Technion, Institute of Technology, Haifa 32000, Israel Abstract.
Mathematical Problems in Image Processing
Gilles Aubert Pierre Kornprobst Mathematical Problems in Image Processing Partial Differential Equations and the Calculus of Variations Second Edition Springer Foreword Preface to the Second Edition Preface
PDE-based image restoration, I: Anti-staircasing and anti-diffusion
PDE-based image restoration, I: Anti-staircasing and anti-diffusion Kisee Joo and Seongjai Kim May 16, 2003 Abstract This article is concerned with simulation issues arising in the PDE-based image restoration
Linear Diffusion. E9 242 STIP- R. Venkatesh Babu IISc
Linear Diffusion Derivation of Heat equation Consider a 2D hot plate with Initial temperature profile I 0 (x, y) Uniform (isotropic) conduction coefficient c Unit thickness (along z) Problem: What is temperature
Introduction to Linear Image Processing
Introduction to Linear Image Processing 1 IPAM - UCLA July 22, 2013 Iasonas Kokkinos Center for Visual Computing Ecole Centrale Paris / INRIA Saclay Image Sciences in a nutshell 2 Image Processing Image
NONLINEAR DIFFUSION PDES
NONLINEAR DIFFUSION PDES Erkut Erdem Hacettepe University March 5 th, 0 CONTENTS Perona-Malik Type Nonlinear Diffusion Edge Enhancing Diffusion 5 References 7 PERONA-MALIK TYPE NONLINEAR DIFFUSION The
Consistent Positive Directional Splitting of Anisotropic Diffusion
In: Boštjan Likar (ed.): Proc. of Computer Vision Winter Workshop, Bled, Slovenia, Feb. 7-9, 2001, pp. 37-48. Consistent Positive Directional Splitting of Anisotropic Diffusion Pavel Mrázek and Mirko Navara
Nonlinear Diffusion. Journal Club Presentation. Xiaowei Zhou
1 / 41 Journal Club Presentation Xiaowei Zhou Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology 2009-12-11 2 / 41 Outline 1 Motivation Diffusion process
A Tensor Variational Formulation of Gradient Energy Total Variation
A Tensor Variational Formulation of Gradient Energy Total Variation Freddie Åström, George Baravdish and Michael Felsberg Linköping University Post Print N.B.: When citing this work, cite the original
NON-LINEAR DIFFUSION FILTERING
NON-LINEAR DIFFUSION FILTERING Chalmers University of Technology Page 1 Summary Introduction Linear vs Nonlinear Diffusion Non-Linear Diffusion Theory Applications Implementation References Page 2 Introduction
Error Analysis for H 1 Based Wavelet Interpolations
Error Analysis for H 1 Based Wavelet Interpolations Tony F. Chan Hao-Min Zhou Tie Zhou Abstract We rigorously study the error bound for the H 1 wavelet interpolation problem, which aims to recover missing
Modulation-Feature based Textured Image Segmentation Using Curve Evolution
Modulation-Feature based Textured Image Segmentation Using Curve Evolution Iasonas Kokkinos, Giorgos Evangelopoulos and Petros Maragos Computer Vision, Speech Communication and Signal Processing Group
Image enhancement by non-local reverse heat equation
Image enhancement by non-local reverse heat equation Antoni Buades 1, Bartomeu Coll 2, and Jean-Michel Morel 3 1 Dpt Matematiques i Informatica Univ. Illes Balears Ctra Valldemossa km 7.5, 07122 Palma
Novel integro-differential equations in image processing and its applications
Novel integro-differential equations in image processing and its applications Prashant Athavale a and Eitan Tadmor b a Institute of Pure and Applied Mathematics, University of California, Los Angeles,
RIGOROUS MATHEMATICAL INVESTIGATION OF A NONLINEAR ANISOTROPIC DIFFUSION-BASED IMAGE RESTORATION MODEL
Electronic Journal of Differential Equations, Vol. 2014 (2014), No. 129, pp. 1 9. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu RIGOROUS MATHEMATICAL
Image Noise: Detection, Measurement and Removal Techniques. Zhifei Zhang
Image Noise: Detection, Measurement and Removal Techniques Zhifei Zhang Outline Noise measurement Filter-based Block-based Wavelet-based Noise removal Spatial domain Transform domain Non-local methods
Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters
Volume 24, N. 1, pp. 131 150, 2005 Copyright 2005 SBMAC ISSN 0101-8205 www.scielo.br/cam Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters
LEVEL SET BASED MULTISPECTRAL SEGMENTATION WITH CORNERS
LEVEL SET BASED MULTISPECTRAL SEGMENTATION WITH CORNERS WENHUA GAO AND ANDREA BERTOZZI Abstract. In this paper we propose an active contour model for segmentation based on the Chan-Vese model. The new
CN780 Final Lecture. Low-Level Vision, Scale-Space, and Polyakov Action. Neil I. Weisenfeld
CN780 Final Lecture Low-Level Vision, Scale-Space, and Polyakov Action Neil I. Weisenfeld Department of Cognitive and Neural Systems Boston University chapter 14.2-14.3 May 9, 2005 p.1/25 Introduction
Research Article Nonlocal Mean Image Denoising Using Anisotropic Structure Tensor
Advances in Optical Technologies Volume 2013, Article ID 794728, 6 pages http://dx.doi.org/10.1155/2013/794728 Research Article Nonlocal Mean Image Denoising Using Anisotropic Structure Tensor Xi Wu, 1,
Energy-Based Image Simplification with Nonlocal Data and Smoothness Terms
Energy-Based Image Simplification with Nonlocal Data and Smoothness Terms Stephan Didas 1, Pavel Mrázek 2, and Joachim Weickert 1 1 Mathematical Image Analysis Group Faculty of Mathematics and Computer
A Localized Linearized ROF Model for Surface Denoising
1 2 3 4 A Localized Linearized ROF Model for Surface Denoising Shingyu Leung August 7, 2008 5 Abstract 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1 Introduction CT/MRI scan becomes a very
Erkut Erdem. Hacettepe University February 24 th, Linear Diffusion 1. 2 Appendix - The Calculus of Variations 5.
LINEAR DIFFUSION Erkut Erdem Hacettepe University February 24 th, 2012 CONTENTS 1 Linear Diffusion 1 2 Appendix - The Calculus of Variations 5 References 6 1 LINEAR DIFFUSION The linear diffusion (heat)
MICROTEXTURE INPAINTING THROUGH GAUSSIAN CONDITIONAL SIMULATION
MICROTEXTURE INPAINTING THROUGH GAUSSIAN CONDITIONAL SIMULATION Bruno Galerne, Arthur Leclaire, Lionel Moisan Université Paris Descartes, MAP5, CNRS UMR 8145, France. CMLA, ENS Cachan, CNRS, Université
Medical Image Analysis
Medical Image Analysis CS 593 / 791 Computer Science and Electrical Engineering Dept. West Virginia University 23rd January 2006 Outline 1 Recap 2 Edge Enhancement 3 Experimental Results 4 The rest of
Computational Photography
Computational Photography Si Lu Spring 208 http://web.cecs.pdx.edu/~lusi/cs50/cs50_computati onal_photography.htm 04/0/208 Last Time o Digital Camera History of Camera Controlling Camera o Photography
A Nonlocal p-laplacian Equation With Variable Exponent For Image Restoration
A Nonlocal p-laplacian Equation With Variable Exponent For Image Restoration EST Essaouira-Cadi Ayyad University SADIK Khadija Work with : Lamia ZIAD Supervised by : Fahd KARAMI Driss MESKINE Premier congrès
Variational Methods in Image Denoising
Variational Methods in Image Denoising Jamylle Carter Postdoctoral Fellow Mathematical Sciences Research Institute (MSRI) MSRI Workshop for Women in Mathematics: Introduction to Image Analysis 22 January
An image decomposition model using the total variation and the infinity Laplacian
An image decomposition model using the total variation and the inity Laplacian Christopher Elion a and Luminita A. Vese a a Department of Mathematics, University of California Los Angeles, 405 Hilgard
A Four-Pixel Scheme for Singular Differential Equations
A Four-Pixel Scheme for Singular Differential Equations Martin Welk 1, Joachim Weickert 1, and Gabriele Steidl 1 Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Bldg. 7 Saarland
Convex Hodge Decomposition of Image Flows
Convex Hodge Decomposition of Image Flows Jing Yuan 1, Gabriele Steidl 2, Christoph Schnörr 1 1 Image and Pattern Analysis Group, Heidelberg Collaboratory for Image Processing, University of Heidelberg,
Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems
Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems Stamatios Lefkimmiatis, Anastasios Roussos 2, Michael Unser, and Petros Maragos 3 Biomedical
ITK Filters. Thresholding Edge Detection Gradients Second Order Derivatives Neighborhood Filters Smoothing Filters Distance Map Image Transforms
ITK Filters Thresholding Edge Detection Gradients Second Order Derivatives Neighborhood Filters Smoothing Filters Distance Map Image Transforms ITCS 6010:Biomedical Imaging and Visualization 1 ITK Filters:
ON THE DISCRETE MAXIMUM PRINCIPLE FOR THE BELTRAMI COLOR FLOW
ON THE DISCRETE MAXIMUM PRINCIPLE FOR THE BELTRAMI COLOR FLOW LORINA DASCAL, ADI DITKOWSKI, AND NIR A. SOCHEN Abstract. We analyze the discrete maximum principle for the Beltrami color flow. The Beltrami
Convex Hodge Decomposition and Regularization of Image Flows
Convex Hodge Decomposition and Regularization of Image Flows Jing Yuan, Christoph Schnörr, Gabriele Steidl April 14, 2008 Abstract The total variation (TV) measure is a key concept in the field of variational
Universität des Saarlandes. Fachrichtung 6.1 Mathematik
Universität des Saarlandes U N I V E R S I T A S S A R A V I E N I S S Fachrichtung 6.1 Mathematik Preprint Nr. 143 PDEs for Tensor Image Processing Joachim Weickert, Christian Feddern, Martin Welk, Bernhard
MICROTEXTURE INPAINTING THROUGH GAUSSIAN CONDITIONAL SIMULATION
MICROTEXTURE INPAINTING THROUGH GAUSSIAN CONDITIONAL SIMULATION Bruno Galerne, Arthur Leclaire, Lionel Moisan Université Paris Descartes, MAP5, CNRS UMR 8145, France. CMLA, ENS Cachan, France. ABSTRACT
Partial Differential Equations and Image Processing. Eshed Ohn-Bar
Partial Differential Equations and Image Processing Eshed Ohn-Bar OBJECTIVES In this presentation you will 1) Learn what partial differential equations are and where do they arise 2) Learn how to discretize
Color Image Enhancement via Chromaticity Diffusion
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO. 5, MAY 2001 701 Color Image Enhancement via Chromaticity Diffusion Bei Tang, Guillermo Sapiro, Member, IEEE, and Vicent Caselles Abstract A novel approach
Complex Diffusion Processes for Image Filtering
Complex Diffusion Processes for Image Filtering Guy Gilboa, Yehoshua Y. Zeevi, and Nir A. Sochen Department of Electrical Engineering, Technion - Israel Institute of Technology Technion City, Haifa 3,
Solution-driven Adaptive Total Variation Regularization
1/15 Solution-driven Adaptive Total Variation Regularization Frank Lenzen 1, Jan Lellmann 2, Florian Becker 1, Stefania Petra 1, Johannes Berger 1, Christoph Schnörr 1 1 Heidelberg Collaboratory for Image
Scale Space Analysis by Stabilized Inverse Diffusion Equations
Scale Space Analysis by Stabilized Inverse Diffusion Equations Ilya Pollak, Alan S. Willsky and Hamid Krim Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 77 Massachusetts
Generalized Newton-Type Method for Energy Formulations in Image Processing
Generalized Newton-Type Method for Energy Formulations in Image Processing Leah Bar and Guillermo Sapiro Department of Electrical and Computer Engineering University of Minnesota Outline Optimization in
A Generative Perspective on MRFs in Low-Level Vision Supplemental Material
A Generative Perspective on MRFs in Low-Level Vision Supplemental Material Uwe Schmidt Qi Gao Stefan Roth Department of Computer Science, TU Darmstadt 1. Derivations 1.1. Sampling the Prior We first rewrite
Fraunhofer Institute for Computer Graphics Research Interactive Graphics Systems Group, TU Darmstadt Fraunhoferstrasse 5, Darmstadt, Germany
Scale Space and PDE methods in image analysis and processing Arjan Kuijper Fraunhofer Institute for Computer Graphics Research Interactive Graphics Systems Group, TU Darmstadt Fraunhoferstrasse 5, 64283
An Improved Nonlinear Model for Image Inpainting
Applied Mathematical Sciences, Vol. 9, 2015, no. 124, 6189-6205 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.58545 An Improved Nonlinear Model for Image Inpainting S. Boujena, K. Bellaj,
Statistical Modeling of Visual Patterns: Part I --- From Statistical Physics to Image Models
Statistical Modeling of Visual Patterns: Part I --- From Statistical Physics to Image Models Song-Chun Zhu Departments of Statistics and Computer Science University of California, Los Angeles Natural images
Nonlinear Diffusion. 1 Introduction: Motivation for non-standard diffusion
Nonlinear Diffusion These notes summarize the way I present this material, for my benefit. But everything in here is said in more detail, and better, in Weickert s paper. 1 Introduction: Motivation for
Designing Partial Differential Equations for Image Processing by Combining Differential Invariants
Designing Partial Differential Equations for Image Processing by Combining Differential Invariants Zhouchen Lin 1 Wei Zhang 2 Xiaoou Tang 2 1 Microsoft Research Asia, zhoulin@microsoft.com 2 The Chinese
Forward-and-Backward Diffusion Processes for Adaptive Image Enhancement and Denoising
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 11, NO. 7, JULY 2002 689 Forward-and-Backward Diffusion Processes for Adaptive Image Enhancement and Denoising Guy Gilboa, Nir Sochen, and Yehoshua Y. Zeevi
Image enhancement. Why image enhancement? Why image enhancement? Why image enhancement? Example of artifacts caused by image encoding
13 Why image enhancement? Image enhancement Example of artifacts caused by image encoding Computer Vision, Lecture 14 Michael Felsberg Computer Vision Laboratory Department of Electrical Engineering 12
TRACKING and DETECTION in COMPUTER VISION Filtering and edge detection
Technischen Universität München Winter Semester 0/0 TRACKING and DETECTION in COMPUTER VISION Filtering and edge detection Slobodan Ilić Overview Image formation Convolution Non-liner filtering: Median
On Mean Curvature Diusion in Nonlinear Image Filtering. Adel I. El-Fallah and Gary E. Ford. University of California, Davis. Davis, CA
On Mean Curvature Diusion in Nonlinear Image Filtering Adel I. El-Fallah and Gary E. Ford CIPIC, Center for Image Processing and Integrated Computing University of California, Davis Davis, CA 95616 Abstract
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. XX, NO. Y, MONTH A General Framework for Low Level Vision. Nir Sochen Ron Kimmel Ravi Malladi
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. XX, NO. Y, MONTH 1999 100 A General Framework for Low Level Vision Nir Sochen Ron Kimmel Ravi Malladi Abstract We introduce a new geometrical framework based
Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering
International Journal of Computer Vision 52(2/3), 189 23, 23 c 23 Kluwer Academic Publishers. Manufactured in The Netherlands. Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering PAVEL
Lecture 8: Interest Point Detection. Saad J Bedros
#1 Lecture 8: Interest Point Detection Saad J Bedros sbedros@umn.edu Last Lecture : Edge Detection Preprocessing of image is desired to eliminate or at least minimize noise effects There is always tradeoff
A NEW PARTIAL DIFFERENTIAL EQUATION-BASED APPROACH FOR 3D DATA DENOISING AND EDGE PRESERVING
A NEW PARTIAL DIFFERENTIAL EQUATION-BASED APPROACH FOR 3D DATA DENOISING AND EDGE PRESERVING SORIN POP 1,, OLIVIER LAVIALLE, 3, ROMULUS TEREBES 1, MONICA BORDA 1 Key words: 3-D filtering, Anisotropic diffusion,
Image Deblurring in the Presence of Impulsive Noise
Image Deblurring in the Presence of Impulsive Noise Leah Bar Nir Sochen Nahum Kiryati School of Electrical Engineering Dept. of Applied Mathematics Tel Aviv University Tel Aviv, 69978, Israel April 18,
Lecture 8: Interest Point Detection. Saad J Bedros
#1 Lecture 8: Interest Point Detection Saad J Bedros sbedros@umn.edu Review of Edge Detectors #2 Today s Lecture Interest Points Detection What do we mean with Interest Point Detection in an Image Goal:
Conjugate gradient acceleration of non-linear smoothing filters
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com Conjugate gradient acceleration of non-linear smoothing filters Knyazev, A.; Malyshev, A. TR25-43 December 25 Abstract The most efficient edge-preserving
Motion Estimation (I) Ce Liu Microsoft Research New England
Motion Estimation (I) Ce Liu celiu@microsoft.com Microsoft Research New England We live in a moving world Perceiving, understanding and predicting motion is an important part of our daily lives Motion
Image Segmentation Using A New Scalar Texture Descriptor based on Extended Structure Tensor
Journal of Information Hiding and Multimedia Signal Processing c 2016 ISSN 2073-4212 Ubiquitous International Volume 7, Number 5, September 2016 Image Segmentation Using A New Scalar Texture Descriptor
SINCE THE elegant formulation of anisotropic diffusion
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 7, NO. 3, MARCH 1998 421 Robust Anisotropic Diffusion Michael J. Black, Member, IEEE, Guillermo Sapiro, Member, IEEE, David H. Marimont, Member, IEEE, and David
A Partial Differential Equation Approach to Image Zoom
A Partial Differential Equation Approach to Image Zoom Abdelmounim Belahmidi and Frédéric Guichard January 2004 Abstract We propose a new model for zooming digital image. This model, driven by a partial
NOISE ENHANCED ANISOTROPIC DIFFUSION FOR SCALAR IMAGE RESTORATION. 6, avenue du Ponceau Cergy-Pontoise, France.
NOISE ENHANCED ANISOTROPIC DIFFUSION FOR SCALAR IMAGE RESTORATION Aymeric HISTACE 1, David ROUSSEAU 2 1 Equipe en Traitement d'image et du Signal UMR CNRS 8051 6, avenue du Ponceau 95014 Cergy-Pontoise,
ENERGY METHODS IN IMAGE PROCESSING WITH EDGE ENHANCEMENT
ENERGY METHODS IN IMAGE PROCESSING WITH EDGE ENHANCEMENT PRASHANT ATHAVALE Abstract. Digital images are can be realized as L 2 (R 2 objects. Noise is introduced in a digital image due to various reasons.
COMS 4721: Machine Learning for Data Science Lecture 19, 4/6/2017
COMS 4721: Machine Learning for Data Science Lecture 19, 4/6/2017 Prof. John Paisley Department of Electrical Engineering & Data Science Institute Columbia University PRINCIPAL COMPONENT ANALYSIS DIMENSIONALITY
A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
J Math Imaging Vis c 27 Springer Science + Business Media, LLC. Manufactured in The Netherlands. DOI: 1.7/s1851-7-652-y A Variational Approach to Reconstructing Images Corrupted by Poisson Noise TRIET
A Dual Formulation of the TV-Stokes Algorithm for Image Denoising
A Dual Formulation of the TV-Stokes Algorithm for Image Denoising Christoffer A. Elo, Alexander Malyshev, and Talal Rahman Department of Mathematics, University of Bergen, Johannes Bruns gate 12, 5007
Lecture 4 Colorization and Segmentation
Lecture 4 Colorization and Segmentation Summer School Mathematics in Imaging Science University of Bologna, Itay June 1st 2018 Friday 11:15-13:15 Sung Ha Kang School of Mathematics Georgia Institute of
Motion Estimation (I)
Motion Estimation (I) Ce Liu celiu@microsoft.com Microsoft Research New England We live in a moving world Perceiving, understanding and predicting motion is an important part of our daily lives Motion
Riemannian Drums, Anisotropic Curve Evolution and Segmentation
Riemannian Drums, Anisotropic Curve Evolution and Segmentation Jayant Shah * Mathematics Department, Northeastern University, Boston, MA 02115. * This work was partially supported by PHS Grant 2-R01 NS34189
Geometric Heat Equation and Nonlinear. Diusion of Shapes and Images. Providence, RI 02912
Geometric Heat Equation and Nonlinear Diusion of Shapes and Images Benjamin B. Kimia Kaleem Siddiqi Division of Engineering Division of Engineering Brown University Brown University kimia@lems.brown.edu
Regular article Nonlinear multigrid methods for total variation image denoising
Comput Visual Sci 7: 199 06 (004) Digital Object Identifier (DOI) 10.1007/s00791-004-0150-3 Computing and Visualization in Science Regular article Nonlinear multigrid methods for total variation image
A Riemannian Framework for Denoising Diffusion Tensor Images
A Riemannian Framework for Denoising Diffusion Tensor Images Manasi Datar No Institute Given Abstract. Diffusion Tensor Imaging (DTI) is a relatively new imaging modality that has been extensively used
Image Deblurring in the Presence of Impulsive Noise
Image Deblurring in the Presence of Impulsive Noise Leah Bar Nir Sochen Nahum Kiryati School of Electrical Engineering Dept. of Applied Mathematics Tel Aviv University Tel Aviv, 69978, Israel Abstract
Courbure discrète : théorie et applications
Courbure discrète : théorie et applications Rencontre organisée par : Laurent Najman and Pascal Romon 18-22 novembre 2013 Yonathan Aflalo, Anastasia Dubrovina, Ron Kimmel, and Aaron Wetzler Curvature in
Edges and Scale. Image Features. Detecting edges. Origin of Edges. Solution: smooth first. Effects of noise
Edges and Scale Image Features From Sandlot Science Slides revised from S. Seitz, R. Szeliski, S. Lazebnik, etc. Origin of Edges surface normal discontinuity depth discontinuity surface color discontinuity
Universität des Saarlandes. Fachrichtung 6.1 Mathematik
Universität des Saarlandes U N I V E R S I T A S S A R A V I E N I S S Fachrichtung 6.1 Mathematik Preprint Nr. 142 Tensor Field Interpolation with PDEs Joachim Weickert and Martin Welk Saarbrücken 2005
Medical Image Analysis
Medical Image Analysis CS 593 / 791 Computer Science and Electrical Engineering Dept. West Virginia University 20th January 2006 Outline 1 Discretizing the heat equation 2 Outline 1 Discretizing the heat
Modeling Multiscale Differential Pixel Statistics
Modeling Multiscale Differential Pixel Statistics David Odom a and Peyman Milanfar a a Electrical Engineering Department, University of California, Santa Cruz CA. 95064 USA ABSTRACT The statistics of natural
Equations of fluid dynamics for image inpainting
Equations of fluid dynamics for image inpainting Evelyn M. Lunasin Department of Mathematics United States Naval Academy Joint work with E.S. Titi Weizmann Institute of Science, Israel. IMPA, Rio de Janeiro
Detectors part II Descriptors
EECS 442 Computer vision Detectors part II Descriptors Blob detectors Invariance Descriptors Some slides of this lectures are courtesy of prof F. Li, prof S. Lazebnik, and various other lecturers Goal:
Fast Local Laplacian Filters: Theory and Applications
Fast Local Laplacian Filters: Theory and Applications Mathieu Aubry (INRIA, ENPC), Sylvain Paris (Adobe), Sam Hasinoff (Google), Jan Kautz (UCL), and Frédo Durand (MIT) Input Unsharp Mask, not edge-aware
Vector Median Filters, Inf-Sup Operations, and Coupled PDE s: Theoretical Connections
Journal of Mathematical Imaging and Vision 8, 109 119 000 c 000 Kluwer Academic Publishers Manufactured in The Netherlands Vector Median Filters, Inf-Sup Operations, and Coupled PDE s: Theoretical Connections
Coordinate Update Algorithm Short Course Operator Splitting
Coordinate Update Algorithm Short Course Operator Splitting Instructor: Wotao Yin (UCLA Math) Summer 2016 1 / 25 Operator splitting pipeline 1. Formulate a problem as 0 A(x) + B(x) with monotone operators
Nonlinear regularizations of TV based PDEs for image processing
Nonlinear regularizations of TV based PDEs for image processing Andrea Bertozzi, John Greer, Stanley Osher, and Kevin Vixie ABSTRACT. We consider both second order and fourth order TV-based PDEs for image
Super-Resolution. Shai Avidan Tel-Aviv University
Super-Resolution Shai Avidan Tel-Aviv University Slide Credits (partial list) Ric Szelisi Steve Seitz Alyosha Efros Yacov Hel-Or Yossi Rubner Mii Elad Marc Levoy Bill Freeman Fredo Durand Sylvain Paris
Variational Methods in Signal and Image Processing
Variational Methods in Signal and Image Processing XU WANG Texas A&M University Dept. of Electrical & Computer Eng. College Station, Texas United States xu.wang@tamu.edu ERCHIN SERPEDIN Texas A&M University
Approximate Inference Part 1 of 2
Approximate Inference Part 1 of 2 Tom Minka Microsoft Research, Cambridge, UK Machine Learning Summer School 2009 http://mlg.eng.cam.ac.uk/mlss09/ Bayesian paradigm Consistent use of probability theory
On Semi-implicit Splitting Schemes for the Beltrami Color Image Filtering
J Math Imaging Vis 2011 40: 199 213 DOI 10.1007/s10851-010-0254-y On Semi-implicit Splitting Schemes for the Beltrami Color Image Filtering Guy Rosman Lorina Dascal Xue-Cheng Tai Ron Kimmel Published online:
Approximate Inference Part 1 of 2
Approximate Inference Part 1 of 2 Tom Minka Microsoft Research, Cambridge, UK Machine Learning Summer School 2009 http://mlg.eng.cam.ac.uk/mlss09/ 1 Bayesian paradigm Consistent use of probability theory
Optimal stopping time formulation of adaptive image filtering
Optimal stopping time formulation of adaptive image filtering I. Capuzzo Dolcetta, R. Ferretti 19.04.2000 Abstract This paper presents an approach to image filtering based on an optimal stopping time problem
Generalized reaction diffusion equations
16 April 1999 Chemical Physics Letters 303 1999 531 536 Generalized reaction diffusion euations G.W. Wei ) Department of Computational Science, National UniÕersity of Singapore, Singapore 11960, Singapore
Convex Generalizations of Total Variation based on the Structure Tensor with Applications to Inverse Problems
Convex Generalizations of Total Variation based on the Structure Tensor with Applications to Inverse Problems Stamatios Lefkimmiatis, Anastasios Roussos 2, Michael Unser, and Petros Maragos 3 Biomedical
Analysis of Numerical Methods for Level Set Based Image Segmentation
Analysis of Numerical Methods for Level Set Based Image Segmentation Björn Scheuermann and Bodo Rosenhahn Institut für Informationsverarbeitung Leibnitz Universität Hannover {scheuerm,rosenhahn}@tnt.uni-hannover.de