Results 1  10
of
81
Total Variation Wavelet Inpainting
 J. Math. Imaging Vision
, 2006
"... We consider the problem of filling in missing or damaged wavelet coe#cients due to lossy image transmission or communication. The task is closely related to classical inpainting problems, but also remarkably di#ers in that the inpainting regions are in the wavelet domain. New challenges include that ..."
Abstract

Cited by 49 (4 self)
 Add to MetaCart
(Show Context)
We consider the problem of filling in missing or damaged wavelet coe#cients due to lossy image transmission or communication. The task is closely related to classical inpainting problems, but also remarkably di#ers in that the inpainting regions are in the wavelet domain. New challenges include that the resulting inpainting regions in the pixel domain are usually not well defined, as well as that degradation is often spatially inhomogeneous. Two novel variational models are proposed to meet such challenges, which combine the total variation (TV) minimization technique with wavelet representations. The associated EulerLagrange equations lead to nonlinear partial di#erential equations (PDE's) in the wavelet domain, and proper numerical algorithms and schemes are designed to handle their computation. The proposed models can have e#ective and automatic control over geometric features of the inpainted images, including the sharpness and curvature information of edges.
Inpainting and the Fundamental Problem of Image Processing
 SIAM News
, 2003
"... ..."
(Show Context)
Variational PDE models in image processing
, 2002
"... This paper is based on a plenary presentation given by Tony F. Chan at the 2002 Joint Mathematical Meeting, San Diego, and has been supported in part by NSF under grant numbers DMS9973341 (Chan), DMS0202565 (Shen), and ITR0113439 (Vese), by ONR under N000140210015 (Chan), and by NIH under NIH ..."
Abstract

Cited by 45 (11 self)
 Add to MetaCart
(Show Context)
This paper is based on a plenary presentation given by Tony F. Chan at the 2002 Joint Mathematical Meeting, San Diego, and has been supported in part by NSF under grant numbers DMS9973341 (Chan), DMS0202565 (Shen), and ITR0113439 (Vese), by ONR under N000140210015 (Chan), and by NIH under NIHP20MH65166 (Chan and Vese). For the preprints and reprints mentioned in this paper, please visit our web site at: www.math.ucla.edu/~imagers. Chan and Vese are with the Department of Mathematics, UCLA, Los Angeles, CA 90095, fchan, lveseg@math.ucla.edu; Shen is with the School of Mathematics, University of Minnesota, Minneapolis, MN 55455, jhshen@math.umn.edu
Variational Image Inpainting
 Comm. Pure Applied Math
, 2005
"... Inpainting is an image interpolation problem, with broad applications in image and vision analysis. This paper presents our recent efforts in developing inpainting models based on the Bayesian and variational principles. We discuss several geometric image models, their role in the construction of va ..."
Abstract

Cited by 37 (6 self)
 Add to MetaCart
(Show Context)
Inpainting is an image interpolation problem, with broad applications in image and vision analysis. This paper presents our recent efforts in developing inpainting models based on the Bayesian and variational principles. We discuss several geometric image models, their role in the construction of variational inpainting models, and the associated EulerLagrange PDEs and their numerical computation.
A WaveletLaplace Variational Technique for Image . . .
 IEEE TRANSACTIONS IN IMAGE PROCESSING
"... We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDEbased techniques involving the GinzburgLandau functional, but using more localized waveletbased methods. We present results for both binary and grayscale images. Comparable speeds are ac ..."
Abstract

Cited by 27 (12 self)
 Add to MetaCart
We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDEbased techniques involving the GinzburgLandau functional, but using more localized waveletbased methods. We present results for both binary and grayscale images. Comparable speeds are achieved with better sharpness of edges in the reconstruction.
Fast Global Optimization of Curvature
"... Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total var ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
(Show Context)
Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total variation or boundary length. A regularization which has received less attention is to minimize the curvature of the solution. One reason why this regularization has received less attention is due to the difficulty in finding an optimal solution to this image model, since many existing methods are complicated, slow and/or provide a suboptimal solution. Following the recent progress of Schoenemann et al. [28], we provide a simple formulation of curvature regularization which admits a fast optimization which gives globally optimal solutions in practice. We demonstrate the effectiveness of this method by applying this curvature regularization to image segmentation. 1.
Action minimization and sharpinterface limits for the stochastic AllenCahn equation
 Commun. Pure Appl. Math
"... ..."
(Show Context)
Level Set Methods and Their Applications in Image Science
 Comm. Math Sci
"... this article, we discuss the question "What Level Set Methods can do for image science". We examine the scope of these techniques in image science, in particular in image segmentation, and introduce some relevant level set techniques that are potentially useful for this class of applicatio ..."
Abstract

Cited by 23 (1 self)
 Add to MetaCart
(Show Context)
this article, we discuss the question "What Level Set Methods can do for image science". We examine the scope of these techniques in image science, in particular in image segmentation, and introduce some relevant level set techniques that are potentially useful for this class of applications. We will show that image science demands multidisciplinary knowledge and flexible but still robust methods. That is why the Level Set Method has become a thriving technique in this field
DIFFUSE INTERFACE MODELS ON GRAPHS FOR CLASSIFICATION OF HIGH DIMENSIONAL DATA
, 2012
"... There are currently several communities working on algorithms for classification of high dimensional data. This work develops a class of variational algorithms that combine recent ideas from spectral methods on graphs with nonlinear edge/region detection methods traditionally used in in the PDEba ..."
Abstract

Cited by 22 (10 self)
 Add to MetaCart
(Show Context)
There are currently several communities working on algorithms for classification of high dimensional data. This work develops a class of variational algorithms that combine recent ideas from spectral methods on graphs with nonlinear edge/region detection methods traditionally used in in the PDEbased imaging community. The algorithms are based on the GinzburgLandau functional which has classical PDE connections to total variation minimization. Convexsplitting algorithms allow us to quickly find minimizers of the proposed model and take advantage of fast spectral solvers of linear graphtheoretic problems. We present diverse computational examples involving both basic clustering and semisupervised learning for different applications. Case studies include feature identification in images, segmentation in social networks, and segmentation of shapes in high dimensional datasets.
CahnHilliard inpainting and a generalization for grayvalue images
 SIAM J. Imaging Sci
"... Abstract. The CahnHilliard equation is a fourth order reaction diffusion equation originating in material science for modeling phase separation and phase coarsening in binary alloys. The inpainting of binary images using the CahnHilliard equation is a new approach in image processing. In this pape ..."
Abstract

Cited by 21 (8 self)
 Add to MetaCart
(Show Context)
Abstract. The CahnHilliard equation is a fourth order reaction diffusion equation originating in material science for modeling phase separation and phase coarsening in binary alloys. The inpainting of binary images using the CahnHilliard equation is a new approach in image processing. In this paper we discuss the stationary state of the proposed model and introduce a generalization for grayvalue images of bounded variation. This is realized by using subgradients of the total variation functional within the flow, which leads to structure inpainting with smooth curvature of level sets. Key words. CahnHilliard equation, TV minimization, image inpainting AMS subject classifications. 49J40 1. Introduction. An important task in image processing is the process of filling in missing parts of damaged images based on the information obtained from the surrounding areas. It is essentially a type of interpolation and is referred to as inpainting. Given an image f in a suitable Banach space of functions defined on Ω ⊂ R2, an open and bounded domain, the problem is to reconstruct the original image u in the damaged domain D ⊂ Ω, called inpainting domain. In