A comparison of three total variation based texture extraction models
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TLDR
This paper qualitatively compares three recently proposed models for signal/image texture extraction based on total variation minimization: the Meyer, Vese-Osher (VO), and TV-L^1[12,38,2-4,29-31] models.About:
This article is published in Journal of Visual Communication and Image Representation.The article was published on 2007-06-01 and is currently open access. It has received 68 citations till now. The article focuses on the topics: Image texture.read more
Figures
Fig. 5. Example 4 and 5, cartoon-texture decomposition: left halves - cartoon, right halves - texture/noise. 
Fig. 1. Example 1: 1D signal decomposition 
Table 1 Mosek termination measures 
Fig. 3. Inputs: (a) original 117×117 fingerprint, (b) original 512×512 Barbara, (c) a 256×256 part of original Barbara, (d) a 256×256 part of noisy Barbara (std.=20), (e) original 256× 256 4texture. 
Fig. 2. Example 1: 1D signal decomposition (continue) 
Fig. 4. Examples 2 and 3, cartoon-texture decomposition results: left halves - cartoon, right halves - texture.
Citations
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Second order decomposition model for image processing : numerical experimentation
TL;DR: This paper is a companion paper of [4] where a second order image decomposition model to perform denoising and texture extraction has been stud-ied and for highly textured images the model gives a two-scale texture decomposition.
Dissertation
Novel high-quality variational image decomposition models and their applications
TL;DR: A novel image decomposition model called Improved Edge Segregation, based on the pioneering work of Vese and Osher, is put forward, which gives better decomposition results, and a new model, called the Simultaneous Decomposition/Discrimination model, is described, also improving decomposition and discrimination quality.
Posted Content
A Dual Alternating Direction Method of Multipliers for Image Decomposition and Restoration.
TL;DR: This paper develops a dual alternating direction method of multipliers (ADMM) for an image decomposition model that gives the cartoon part and the texture part of an image but also gives the restored image.
Book ChapterDOI
Multiscale analysis of volumetric motion field using general order prior
TL;DR: Variational optical flow computation involving the prior with the fractional order differentiations on optical flow vectors allows us to detect discontinuity of optical flow using linear operations.
Journal ArticleDOI
Multi-Phase Image Segmentation Based on Low-Rank Prior Decomposition
TL;DR: In this paper , a multi-region image segmentation model based on low-rank prior decomposition is proposed, which uses a low rank prior to characterize the texture component, and the total variational norm to characterise the piecewise smooth structure component.
References
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Journal ArticleDOI
Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
Journal ArticleDOI
Second-order cone programming
Farid Alizadeh,Donald Goldfarb +1 more
TL;DR: SOCP formulations are given for four examples: the convex quadratically constrained quadratic programming (QCQP) problem, problems involving fractional quadRatic functions, and many of the problems presented in the survey paper of Vandenberghe and Boyd as examples of SDPs can in fact be formulated as SOCPs and should be solved as such.
MonographDOI
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
TL;DR: It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincare inequalities.
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Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
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