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 convex-nonconvex variational method for the additive decomposition of functions on surfaces
Journal ArticleDOI
A new nonlocal variational setting for image processing
Yan Jin,Jürgen Jost,Guofang Wang +2 more
TL;DR: In this paper, a nonlocal variational scheme for image denoising is proposed based on the nonlocal means filter and the non-local TV model proposed by Gilboa-Osher by using nonlocal operators.
Posted Content
Noise2Kernel: Adaptive Self-Supervised Blind Denoising using a Dilated Convolutional Kernel Architecture.
Kanggeun Lee,Won-Ki Jeong +1 more
TL;DR: A dilated convolutional network is proposed that satisfies an invariant property, allowing efficient kernel-based training without random masking, and an adaptive self-supervision loss is proposed to circumvent the requirement of zero-mean constraint.
Proceedings ArticleDOI
Coupled geometric and texture PDE-based segmentation
TL;DR: Experimental results on various classes of images such as soilsections, aerial and natural scenes indicate that the combined effect of image decomposition and multi-cue segmentation improves the overall segmentation process.
Dissertation
Stochastic Image Models and Texture Synthesis
TL;DR: A new algorithm for procedural texture synthesis from example relying on the recent Gabor noise model permits to automatically compute procedural models for real-world micro-textures.
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.