Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
Chambolle, Antonin (1995), Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations, SIAM Journal on Applied Mathematics, 55, 3, p. 827-863. http://dx.doi.org/10.1137/S0036139993257132
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Applied Mathematics
MetadataShow full item record
Abstract (EN)In this paper we discuss the links between Mumford and Shah’s variational problem for (signal and) image segmentation, based on an energy functional of a continuous grey-level function, and the numerical algorithms proposed to solve it. These numerical approaches are based on a discrete functional. We recall that, in one dimension, this discrete functional is asymptotically equivalent to the continuous functional. This can be summarized in a $\Gamma $-convergence result. We show that the same result holds in dimension two, provided that the continuous energy is adapted to the anisotropy of the discrete approaches. We display a few experimental results in dimensions one and two.
Subjects / Keywordstheory and algorithms for image segmentation; variational problems; special bounded variation functions; Γ-convergence; Hausdorff measures
Showing items related by title and author.
Nonlinear Wavelet Image Processing: Variational Problems, Compression, and Noise Removal through Wavelet Shrinkage Chambolle, Antonin; DeVore, Ron; Lee, Nam-Yong; Lucier, Bradley J. (1998) Article accepté pour publication ou publié