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Journal Articles IEEE Transactions on Image Processing Year : 2019

Semi-Linearized Proximal Alternating Minimization for a Discrete Mumford-Shah Model

Abstract

The Mumford-Shah model is a standard model in image segmentation, and due to its difficulty , many approximations have been proposed. The major interest of this functional is to enable joint image restoration and contour detection. In this work, we propose a general formulation of the discrete counterpart of the Mumford-Shah functional, adapted to nonsmooth penalizations, fitting the assumptions required by the Proximal Alternating Linearized Minimization (PALM), with convergence guarantees. A second contribution aims to relax some assumptions on the involved functionals and derive a novel Semi-Linearized Proximal Alternated Minimization (SL-PAM) algorithm, with proved convergence. We compare the performances of the algorithm with several nonsmooth penalizations, for Gaussian and Poisson denoising, image restoration and RGB-color denoising. We compare the results with state-of-the-art convex relaxations of the Mumford-Shah functional, and a discrete version of the Ambrosio-Tortorelli functional. We show that the SL-PAM algorithm is faster than the original PALM algorithm, and leads to competitive denoising, restoration and segmentation results.
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Dates and versions

hal-01782346 , version 1 (01-05-2018)
hal-01782346 , version 2 (06-12-2018)
hal-01782346 , version 3 (15-07-2019)
hal-01782346 , version 4 (03-02-2020)

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Cite

Marion Foare, Nelly Pustelnik, Laurent Condat. Semi-Linearized Proximal Alternating Minimization for a Discrete Mumford-Shah Model. IEEE Transactions on Image Processing, 2019, pp.1-13. ⟨10.1109/TIP.2019.2944561⟩. ⟨hal-01782346v4⟩
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