Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
DOI: 10.1137/S0036139993257132
关键词: Dimension (vector space) 、 Function (mathematics) 、 Applied mathematics 、 Γ-convergence 、 Numerical analysis 、 Mumford–Shah functional 、 Mathematics 、 Image processing 、 Energy functional 、 Image segmentation 、 Topology
摘要: 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, numerical algorithms proposed to solve it. These approaches are discrete functional. We recall that, in one dimension, is asymptotically equivalent This can be summarized $\Gamma $-convergence result. show that same result holds dimension two, provided adapted anisotropy approaches. display few experimental results dimensions two.
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