A comparison of three total variation based texture extraction models

Authors:
Wotao Yin;Donald Goldfarb;Stanley Osher
Affiliations:
Rice University, Department of Computational and Applied Mathematics, 6100 Main St, MS-134, Houston, TX 77005, USA;Columbia University, Department of Industrial Engineering and Operations Research, 500 West 120th St, Mudd 313, New York, NY 10027, USA;UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095, USA
Venue:
Journal of Visual Communication and Image Representation
Year:
2007

Citing 24
Cited 11

Weakly differentiable functions

Weakly differentiable functions
Nonlinear total variation based noise removal algorithms

Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

SIAM Journal on Numerical Analysis
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing

Journal of Scientific Computing
An Algorithm for Total Variation Minimization and Applications

Journal of Mathematical Imaging and Vision
A Variational Approach to Remove Outliers and Impulse Noise

Journal of Mathematical Imaging and Vision
Weakly Constrained Minimization: Application to the Estimation of Images and Signals Involving Constant Regions

Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models

International Journal of Computer Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component

Journal of Mathematical Imaging and Vision
Illumination Normalization for Face Recognition and Uneven Background Correction Using Total Variation Based Image Models

CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Background correction for cDNA microarray images using the TV+L1 model

Bioinformatics
Second-order Cone Programming Methods for Total Variation-Based Image Restoration

SIAM Journal on Scientific Computing
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection

International Journal of Computer Vision
Denoising by BV-duality

Journal of Scientific Computing
Total Variation Models for Variable Lighting Face Recognition

IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

Journal of Mathematical Imaging and Vision
Total variation minimization and a class of binary MRF models

EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Image cartoon-texture decomposition and feature selection using the total variation regularized L1 functional

VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
A new coarse-to-fine framework for 3d brain MR image registration

CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
Recursive median filters of increasing order: a variationalapproach

IEEE Transactions on Signal Processing
A property of the minimum vectors of a regularizing functionaldefined by means of the absolute norm

IEEE Transactions on Signal Processing
Digital filters as absolute norm regularizers

IEEE Transactions on Signal Processing
Image decomposition via the combination of sparse representations and a variational approach

IEEE Transactions on Image Processing

Projected Gradient Based Color Image Decomposition

SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Computing the Local Continuity Order of Optical Flow Using Fractional Variational Method

EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

Journal of Mathematical Imaging and Vision
Fast cartoon + texture image filters

IEEE Transactions on Image Processing
Continuity order of local displacement in volumetric image sequence

WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
Multiscale analysis of volumetric motion field using general order prior

ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
Deconvolving Poissonian images by a novel hybrid variational model

Journal of Visual Communication and Image Representation
Image decomposition via learning the morphological diversity

Pattern Recognition Letters
Geometry of total variation regularized Lp-model

Journal of Computational and Applied Mathematics
A full second order variational model for multiscale texture analysis

Computational Optimization and Applications
Sparse representation with morphologic regularizations for single image super-resolution

Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper qualitatively compares three recently proposed models for signal/image texture extraction based on total variation minimization: the Meyer [27], Vese-Osher (VO) [35], and TV-L^1[12,38,2-4,29-31] models. We formulate discrete versions of these models as second-order cone programs (SOCPs) which can be solved efficiently by interior-point methods. Our experiments with these models on 1D oscillating signals and 2D images reveal their differences: the Meyer model tends to extract oscillation patterns in the input, the TV-L^1 model performs a strict multiscale decomposition, and the Vese-Osher model has properties falling in between the other two models.