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)

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