A full second order variational model for multiscale texture analysis

Authors:
Maïtine Bergounioux;Loïc Piffet
Affiliations:
UFR Sciences, Math., Labo. MAPMO, UMR 7349, Université d'Orléans, Orléans cedex 2, France 45067;UFR Sciences, Math., Labo. MAPMO, UMR 7349, Université d'Orléans, Orléans cedex 2, France 45067
Venue:
Computational Optimization and Applications
Year:
2013

Citing 11
Cited 0

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
Convex analysis and variational problems

Convex analysis and variational problems
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
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing

Journal of Scientific Computing
Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions

Journal of Mathematical Imaging and Vision
An Algorithm for Total Variation Minimization and Applications

Journal of Mathematical Imaging and Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component

Journal of Mathematical Imaging and Vision
Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (Mps-Siam Series on Optimization 6)

Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (Mps-Siam Series on Optimization 6)
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A comparison of three total variation based texture extraction models

Journal of Visual Communication and Image Representation
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a second order image decomposition model to perform denoising and texture extraction. We look for the decomposition f=u+v+w where u is a first order term, v a second order term and w the (0 order) remainder term. For highly textured images the model gives a two-scale texture decomposition: u can be viewed as a macro-texture (larger scale) whose oscillations are not too large and w is the micro-texture (very oscillating) that may contain noise. We perform mathematical analysis of the model and give numerical examples.