Abstract
Morel and Solimini have established proofs of important properties of segmentations which can be seen as locally optimal for the simplest Mumford-Shah model in the continuous domain. A weakness of the latter is that it is not suitable for handling noisy images. We propose a Bayesian model to overcome these problems. We demonstrate that this Bayesian model indeed generalizes the original Mumford-Shah model, and we prove it has the same desirable properties as shown by Morel and Solimini.
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Trevor Tao was Born in 1977 in Adelaide, Australia, found to be autistic when he was two years old. He was the first autistic child in Australia to have started normal school at the same age as his peers. He later became interested in music, chess, and mathematics. He has been described as a musical savant, and has represented Australia in the International Chess Olympiad in 1994, and won a bronze medal in the International Mathematical Olympiad in 1995. In 2000 he completed a double degree in B.Sc (Mathematics & Computer Science) and B.Mus. (Performance & Composition) at the University of Adelaide. After a short vacation job at the Defence Science & Technology Organization in Adelaide, he became interested in Image Analysis, and studied for a Ph.D. in Applied Mathematics. He is expected to complete his thesis this year.
Dr David J. Crisp graduated from the University of Adelaide (Australia) in 1993 with a Ph.D. in Mathematics. He held several different research positions from 1994 to 1998. In 1999 he joined Australia’s Defence Science & Technology Organisation (DSTO) as a research scientist. His current research at DSTO is focused on the automated detection of targets in synthetic aperture radar imagery.
Dr John van der Hoek graduated from University of Adelaide (Australia) in 1975 with a PhD in Pure Mathematics. He is currently a senior lecturer in the Department of Applied Mathematics at University of Adelaide. His research interests are applied functional analysis, partial differential equations and free boundary value problems, stochastic processes, mathematical finance and signal processing.
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Tao, T.CY., Crisp, D.J. & van der Hoek, J. Mathematical Analysis of An Extended Mumford-Shah Model for Image Segmentation. J Math Imaging Vis 24, 327–340 (2006). https://doi.org/10.1007/s10851-005-3631-1
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DOI: https://doi.org/10.1007/s10851-005-3631-1