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A novel dual-based ADMM to the Chan-Vese model

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Abstract

The level set method is a classical method to solve the Chan-Vese model for the binary image segmentation problem. Some efficient methods such as the convex relaxed methods and the steep descent methods based on a suitable constraint have been proposed to overcome the singularity of the LSM. However, the effectiveness of using these schemes is still limited by the chosen threshold value or the Courant-Friedrichs-Lewy condition. To this end, this paper, based on the Lagrangian dual scheme from the numerical optimization theory, proposes a novel numerical method to solve the CV model. Specifically, the binary constraint of the level set function can be transformed into a nonsmooth optimization problem via the help of the Lagrangian dual scheme. Then the Dual-based Alternating Direction of Method of Multipliers can be employed to solve this transform form. Numerical experiments show that the average (± std.dev) Segmentation Error (SE) of the proposed method on two groups of synthetic images are 5.59%(± 0.19%) and 5.01%(± 3.61%). The Precision, Segmentation Accuracy (SA) and F1-Score (F1S) of natural gray and natural color image reach 75.17%(± 12.42%), 98.87%(± 1.16%), 94.99%(± 5.23%) and 81.91%(± 14.85%), 98.38%(± 0.99%), 86.39%(± 11.72%), respectively, which are better than the other three comparison schemes. Therefore, our proposed method is more robust to initialization, faster and more accurate than three classical methods to solve the CV model.

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Notes

  1. For convenience in the following, the variable x in the functions f(x) and ϕ(x) is omitted without any confusion.

  2. p is a subgradient of a convex function g(x) at x0 ∈domg if g(x) − g(x0) ≥〈p,x −x0〉 for ∀x0 ∈domg.

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Acknowledgements

The authors also thank the anonymous referees for both the careful reading of their manuscript and the very helpful comments and suggestions.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Henan University, Kaifeng, 475004, Henan Province, China

    Zhi-Feng Pang & Lin-Lin Fan

  2. Henan Provincial People’s Hospital, Zhengzhou, 450003, Henan Province, China

    Hao-Hui Zhu

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  1. Zhi-Feng Pang
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  2. Lin-Lin Fan
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  3. Hao-Hui Zhu
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Correspondence to Hao-Hui Zhu.

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This work was partially supported by Science and Technology Major Project of Henan Province (No. 221100310200), Scientific and Technological Project in Henan Province (No. 212102210511) Natural Science Foundation of Henan province(No.232300420108) Natural Science Foundation of China (No. 12071345), Health Commission of Henan Province (No. Wjlx2020380), 2021 Henan Health Young and Middle-aged Discipline Leader Cultivation Project.

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Pang, ZF., Fan, LL. & Zhu, HH. A novel dual-based ADMM to the Chan-Vese model. Multimed Tools Appl 82, 40149–40166 (2023). https://doi.org/10.1007/s11042-023-14707-4

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  • DOI: https://doi.org/10.1007/s11042-023-14707-4

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