{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T10:49:35Z","timestamp":1770461375848,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"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":["62172135"],"award-info":[{"award-number":["62172135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62176084"],"award-info":[{"award-number":["62176084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["PA2021GDSK0092"],"award-info":[{"award-number":["PA2021GDSK0092"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["62172135"],"award-info":[{"award-number":["62172135"]}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["62176084"],"award-info":[{"award-number":["62176084"]}]},{"name":"Fundamental Research Funds for the Central Universities of China","award":["PA2021GDSK0092"],"award-info":[{"award-number":["PA2021GDSK0092"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Mesh denoising is a classical task in mesh processing. Many state-of-the-art methods are still unable to quickly and robustly denoise multifarious noisy 3D meshes, especially in the case of high noise. Recently, neural network-based models have played a leading role in natural language, audio, image, video, and 3D model processing. Inspired by these works, we propose a data-driven mesh denoising method based on recurrent neural networks, which learns the relationship between the feature descriptors and the ground-truth normals. The recurrent neural network has a feedback loop before entering the output layer. By means of the self-feedback of neurons, the output of a recurrent neural network is related not only to the current input but also to the output of the previous moments. To deal with meshes with various geometric features, we use k-means to cluster the faces of the mesh according to geometric similarity and train neural networks for each category individually in the offline learning stage. Each network model, acting similar to a normal regression function, will map the geometric feature descriptor of each facet extracted from the mesh to the denoised facet normal. Then, the denoised normals are used to calculate the new feature descriptors, which become the input of the next similar regression model. In this system, three normal regression modules are cascaded to generate the last facet normals. Lastly, the model\u2019s vertex positions are updated according to the denoised normals. A large number of visual and numerical results have demonstrated that the proposed model outperforms the state-of-the-art methods in most cases.<\/jats:p>","DOI":"10.3390\/sym14061233","type":"journal-article","created":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T01:39:54Z","timestamp":1655257194000},"page":"1233","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Mesh Denoising Based on Recurrent Neural Networks"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8076-0805","authenticated-orcid":false,"given":"Yan","family":"Xing","sequence":"first","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Jieqing","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Peilin","family":"Hong","sequence":"additional","affiliation":[{"name":"School of Medical Information Engineering, Anhui University of Chinese Medicine, Hefei 230012, China"}]},{"given":"Yeyuan","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2122-0240","authenticated-orcid":false,"given":"Min","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Information Engineering, Hefei University of Technology, Hefei 230602, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Taubin, G. 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