Journal ArticleDOI
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Luminita A. Vese,Stanley Osher +1 more
Reads0
Chats0
TLDR
This paper decomposes a given (possible textured) image f into a sum of two functions u+v, where u∈BV is a function of bounded variation (a cartoon or sketchy approximation of f), while v is afunction representing the texture or noise.Abstract:
This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, we decompose a given (possible textured) image f into a sum of two functions u+v, where u∈BV is a function of bounded variation (a cartoon or sketchy approximation of f), while v is a function representing the texture or noise. To model v we use the space of oscillating functions introduced by Yves Meyer, which is in some sense the dual of the BV space. The new algorithm is very simple, making use of differential equations and is easily solved in practice. Finally, we implement the method by finite differences, and we present various numerical results on real textured images, showing the obtained decomposition u+v, but we also show how the method can be used for texture discrimination and texture segmentation.read more
Citations
More filters
Journal ArticleDOI
A New Method of Image Denoising Based on the Energy Method
Shuang Liang,Shuli Wang,Yu Wang +2 more
TL;DR: A new denoising method with edge diffusion along the tangential direction directly is proposed and the performance of this method is tested by single images in this thesis.
Cartoon-texture image decomposition using block wise low-rank texture characterization
TL;DR: AnImagedecomposition method that can viably deteriorates a picture into its cartoon and composition segments by utilizing a portrayal of surface is proposed, which improves it deliver results than cutting edge disintegration models.
Proceedings ArticleDOI
Improvement on Image Decomposition Based on Morphological Component Analysis
Bin Yao,Ling-xiang Yang +1 more
TL;DR: Wang et al. as discussed by the authors used non sub sampled contour let transform to represent structure parts, and double density wavelet transform for the texture parts, then the Besov semi-norm is added for restricting structure parts.
Journal ArticleDOI
Nonconvex variational approach for simultaneously recovering cartoon and texture images
TL;DR: In this paper , a nonconvex variational image decomposition model was proposed for simultaneously recovering cartoon and texture images, where the G-norm was used as an oscillating prior for the texture image.
Book ChapterDOI
On Carathéodory Quasilinear Functionals for BV Functions and Their Time Flows for a Dual \( H^{1}\) Penalty Model for Image Restoration
TL;DR: In this paper, the authors extend the theory of functionals defined on BV space by including certain Caratheodory functions for functionals of the form ''varphi (x,\mathbf {p)}'' in the model of the dual penalty model with integral constraint.
References
More filters
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
Scale-space and edge detection using anisotropic diffusion
Pietro Perona,Jitendra Malik +1 more
TL;DR: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced, chosen to vary spatially in such a way as to encourage intra Region smoothing rather than interregion smoothing.
Journal ArticleDOI
Active contours without edges
Tony F. Chan,Luminita A. Vese +1 more
TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
Book
Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
Journal ArticleDOI
Optimal approximations by piecewise smooth functions and associated variational problems
David Mumford,Jayant Shah +1 more
TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.