{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:33:31Z","timestamp":1760060011518,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61401058","2024-MS-166","JYTMS20230010"],"award-info":[{"award-number":["61401058","2024-MS-166","JYTMS20230010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"General Program of Liaoning Natural Science Foundation","award":["61401058","2024-MS-166","JYTMS20230010"],"award-info":[{"award-number":["61401058","2024-MS-166","JYTMS20230010"]}]},{"name":"Basic Scientific Research Project of the Liaoning Provincial Department of Education","award":["61401058","2024-MS-166","JYTMS20230010"],"award-info":[{"award-number":["61401058","2024-MS-166","JYTMS20230010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Point cloud denoising is essential for improving 3D data quality, yet traditional K-means methods relying on Euclidean distance struggle with non-uniform noise. This paper proposes a K-means algorithm leveraging Total Bregman Divergence (TBD) to better model geometric structures on manifolds, enhancing robustness against noise. Specifically, TBDs\u2014Total Logarithm, Exponential, and Inverse Divergences\u2014are defined on symmetric positive-definite matrices, each tailored to capture distinct local geometries. Theoretical analysis demonstrates the bounded sensitivity of TBD-induced means to outliers via influence functions, while anisotropy indices quantify structural variations. Numerical experiments validate the method\u2019s superiority over Euclidean-based approaches, showing effective noise separation and improved stability. This work bridges geometric insights with practical clustering, offering a robust framework for point cloud preprocessing in vision and robotics applications.<\/jats:p>","DOI":"10.3390\/sym17081186","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T14:11:44Z","timestamp":1753366304000},"page":"1186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A K-Means Clustering Algorithm with Total Bregman Divergence for Point Cloud Denoising"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1863-9294","authenticated-orcid":false,"given":"Xiaomin","family":"Duan","sequence":"first","affiliation":[{"name":"School of Science, Dalian Jiaotong University, Dalian 116028, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3688-2558","authenticated-orcid":false,"given":"Anqi","family":"Mu","sequence":"additional","affiliation":[{"name":"School of Science, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Xinyu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Yuqi","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Science, Dalian Jiaotong University, Dalian 116028, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xiao, K., Li, T., Li, J., Huang, D., and Peng, Y. 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