A Convergent Iterative Support Shrinking Algorithm for Non-Lipschitz Multi-phase Image Labeling Model

The non-Lipschitz piecewise constant Mumford–Shah model has been shown effective for image labeling and segmentation problems [ 33 ], where the non-Lipschitz isotropic ℓ p ( 0 < p < 1 ) regularization term can possess strong abilities to maintain sharp edges. However, the Alternating Direction...

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Veröffentlicht in:Journal of scientific computing Jg. 96; H. 2; S. 47
Hauptverfasser: Yang, Yijie, Li, Yutong, Wu, Chunlin, Duan, Yuping
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2023
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Convergence
Image segmentation
Iterative methods
Labeling
Lower bounds
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Multiphase
Optimization techniques
Regularization
Theoretical
Simplex constraint
68U10
Lower bound theory
Kurdyka–Łojasiewicz property
94A08
Image labeling
Non-Lipschitz optimization
ISSN:0885-7474, 1573-7691
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Zusammenfassung:The non-Lipschitz piecewise constant Mumford–Shah model has been shown effective for image labeling and segmentation problems [ 33 ], where the non-Lipschitz isotropic ℓ p ( 0 < p < 1 ) regularization term can possess strong abilities to maintain sharp edges. However, the Alternating Direction Method of Multiplier (ADMM)-based algorithm used in [ 33 ] lacks the convergence guarantee. In this work, we propose an iterative support shrinking algorithm with proximal linearization for multi-phase image labeling problems, which is theoretically proven to be globally convergent. A key step is that we prove a lower bound theory for the nonzero entries of the gradient of the iterative sequence when both box constraint and simplex constraint are involved in the target energy minimization problem. To the best of our knowledge, this is the first theoretical attempt at the non-Lipschitz piecewise constant Mumford–Shah model. Numerical experiments are conducted on both two-phase and multi-phase labeling problems to indicate the efficiency and effectiveness of the proposed algorithm.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02268-5