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An Estimation Theoretical View on Ambrosio‐Tortorelli Image Segmentation
Author(s) -
Krajsek Kai,
Dedovic Ines,
Scharr Hanno
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210359
Subject(s) - maximum a posteriori estimation , gaussian , probability density function , segmentation , mathematics , a priori and a posteriori , image (mathematics) , point (geometry) , markov random field , prior probability , random field , artificial intelligence , posterior probability , computer science , image segmentation , statistics , maximum likelihood , bayesian probability , physics , philosophy , geometry , epistemology , quantum mechanics
In this paper, we examine the Ambrosio‐Tortorelli (AT) functional [1] for image segmentation from an estimation theoretical point of view. Instead of considering a single point estimate, i.e. the maximum‐a‐posteriori (MAP) estimate, we adopt a wider estimation theoretical view‐point, meaning we consider images to be random variables and investigate their distribution. We derive an effective block‐Gibbs‐sampler for this posterior probability density function (PDF) based on the theory of Gaussian Markov random fields (GMRF) [2]. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)