An ADMM Approach of a Nonconvex and Nonsmooth Optimization Model for Low-Light or Inhomogeneous Image Segmentation

Zheyuan Xing (), Tingting Wu and Junhong Yue ()
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Zheyuan Xing: College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China
Tingting Wu: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
Junhong Yue: College of Date Science, Taiyuan University of Technology, Taiyuan 030024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 03, 1-29

Abstract: In this paper, we propose a novel nonconvex and nonsmooth optimization model for low-light or inhomogeneous image segmentation which is a hybrid of Mumford–Shah energy functional and Retinex theory. The given image is decomposed into the reflectance component and the illumination component by solving Retinex-based Mumford–Shah model with L1 − 𠜃L2 regularizer. Indeed, the existence of the L1 − 𠜃L2 regularizer means the nonsmooth term in the model is nonconvex. Thus, it is difficult to solve the proposed model directly. An alternating direction method of multipliers (ADMM) algorithm is developed to solve the proposed nonconvex and nonsmooth model. We apply a novel splitting technique in our algorithm to ensure that all subproblems admit closed-form solutions. Theoretically, we prove that the sequence generated by our proposed algorithm converges to a stationary point under mild conditions. Next, once the reflectance is obtained, the K-means clustering method is utilized to complete the segmentation. We compare the proposed Retinex-based method with other state-of-the-art segmentation methods under special lighting conditions. Experimental results show that the proposed method has better performance for both gray-scale images and color images efficiently in terms of the quantitative and qualitative results.

Keywords: Nonconvex and nonsmooth optimization; alternating direction method of multipliers (ADMM); image segmentation; intensity inhomogeneity; Retinex (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500215

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