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Quadratic surface center-based possibilistic fuzzy clustering with kernel metric and local information for image segmentation

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Abstract

Kernel fuzzy weighted local information c-means (KWFLICM) algorithm has good segmentation effect in segmenting noisy images, but it can not effectively segment images with low contrast or high noise. The improved algorithm of KWFLICM is a kernel possibilistic fuzzy c-means clustering with local information (KWPFLICM), which has better anti-noise performance. However, this algorithm loses more details of original image when segmenting the image. In this paper, a kernel-based possibilistic fuzzy local information clustering algorithm based on quadratic polynomial is proposed to overcome the shortcomings of KWPFLICM algorithm. At the same time, the local membership information of neighborhood pixels is introduced as the penalty factor to update the local information, so as to further improve the robustness of the algorithm. By optimizing the objective function of modified possibilistic fuzzy local information clustering with quadratic surface centers, the formulas of fuzzy membership, possibilistic typicality, and the coefficients of quadratic polynomial center are derived theoretically, and the convergence of the proposed algorithm is strictly proved by Zangwill theorem and bordered Hessian matrix. Experimental results show that compared with existing state-of-the-art fuzzy clustering-related algorithms, the proposed algorithm has better segmentation performance and stronger anti-noise robustness, and can effectively suppress noise and retain details. It will have far-reaching significance for the development of robust fuzzy clustering segmentation theory.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant numbers 61671377), and the Natural Science Foundation of Shaanxi Province (2022JM-370). Wu and Liu would like to thank the anonymous reviewers for their constructive suggestions to improve the overall quality of the paper.

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  1. School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, 710121, People’s Republic of China

    Chengmao Wu & Zeren Wang

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Chengmao Wu: Conceptualization, Methodology, Visualization, Investigation. Zeren Wang: Data curation, Writing – original draft, Software, Validation, Writing – review & editing.

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Correspondence to Zeren Wang.

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Wu, C., Wang, Z. Quadratic surface center-based possibilistic fuzzy clustering with kernel metric and local information for image segmentation. Multimed Tools Appl 83, 44147–44191 (2024). https://doi.org/10.1007/s11042-023-15267-3

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