Abstract:
The Mumford-Shah model, a standard image segmentation model, has many approximations due to its difficulty. This functional allows image restoration and contour detection.
We propose a general formulation of the discrete counterpart of the Mumford-Shah functional for nonsmooth penalizations, fitting the assumptions of Proximal Alternating Linearized Minimization (PALM) with convergence guarantees.
A second contribution relaxes functional assumptions and derives a new Semi-Linearized Proximal Alternated Minimization (SL-PAM) algorithm with proven convergence.
The algorithm is compared to nonsmooth penalizations for Gaussian, Poisson, image restoration, and RGB-color denoising. We compare the results with state-of-the-art convex Mumford-Shah relaxations and a discrete Ambrosio-Tortorelli functional. SL-PAM outperforms PALM in denoising, restoration, and segmentation.
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