Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms
Year: 2023
Author: Weina Wang, Nannan Tian, Chunlin Wu
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 588–622
Abstract
Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2108-m2021-0057
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 588–622
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Nonconvex nonsmooth regularization Characteristic function Box constraints Support shrinking alternating minimization Kurdyka- Lojasiewicz property Image segmentation.
Author Details
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A Convergent Iterative Support Shrinking Algorithm for Non-Lipschitz Multi-phase Image Labeling Model
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Li, Yutong
Wu, Chunlin
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https://doi.org/10.1007/s10915-023-02268-5 [Citations: 0]