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From Mumford–Shah to Perona–Malik in image processing
Author(s) -
Kawohl B.
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.564
Subject(s) - anisotropic diffusion , mathematics , connection (principal bundle) , image processing , image (mathematics) , diffusion , algorithm , diffusion equation , artificial intelligence , mathematical analysis , computer vision , computer science , geometry , physics , economy , economics , thermodynamics , service (business)
In mathematical image processing we are often presented with amazing examples of image enhancement algorithms. Yet, when applied to different noisy images, they can produce unwanted effects. The analysis of such algorithms lags behind their intuitive development. Two essentially different models have found wide recognition: a variational approach due to Mumford and Shah, and an anisotropic diffusion approach leading to an evolution type equation by Perona and Malik. In this survey we shall explain a surprising connection between these two approaches. Copyright © 2004 John Wiley & Sons, Ltd.