{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T21:20:41Z","timestamp":1767993641309,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2022,8,27]],"date-time":"2022-08-27T00:00:00Z","timestamp":1661558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea (NRF)","doi-asserted-by":"publisher","award":["NRF-2022R1F1A1076095"],"award-info":[{"award-number":["NRF-2022R1F1A1076095"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Three-dimensional mesh post-processing is an important task because low-precision hardware and a poor capture environment will inevitably lead to unordered point clouds with unwanted noise and holes that should be suitably corrected while preserving the original shapes and details. Although many 3D mesh data-processing approaches have been proposed over several decades, the resulting 3D mesh often has artifacts that must be removed and loses important original details that should otherwise be maintained. To address these issues, we propose a novel 3D mesh completion and denoising system with a deep learning framework that reconstructs a high-quality mesh structure from input mesh data with several holes and various types of noise. We build upon SpiralNet by using a variational deep autoencoder with anisotropic filters that apply different convolutional filters to each vertex of the 3D mesh. Experimental results show that the proposed method enhances the reconstruction quality and achieves better accuracy compared to previous neural network systems.<\/jats:p>","DOI":"10.3390\/s22176457","type":"journal-article","created":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T01:37:55Z","timestamp":1661823475000},"page":"6457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Anisotropic SpiralNet for 3D Shape Completion and Denoising"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3467-9758","authenticated-orcid":false,"given":"Seong Uk","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Interdisciplinary Graduate Program in Medical Bigdata Convergence, Kangwon National University, Chuncheon 24341, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jihyun","family":"Roh","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Interdisciplinary Graduate Program in Medical Bigdata Convergence, Kangwon National University, Chuncheon 24341, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3901-0834","authenticated-orcid":false,"given":"Hyeonseung","family":"Im","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Interdisciplinary Graduate Program in Medical Bigdata Convergence, Kangwon National University, Chuncheon 24341, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6637-8215","authenticated-orcid":false,"given":"Jongmin","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Interdisciplinary Graduate Program in Medical Bigdata Convergence, Kangwon National University, Chuncheon 24341, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, Y., Guo, W., Shen, J., Wu, Z., and Zhang, Q. (2022). Motion-Induced Phase Error Compensation Using Three-Stream Neural Networks. Appl. Sci., 12.","DOI":"10.3390\/app12168114"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Rizzi, C., Campana, F., Bici, M., Gherardini, F., Ingrassia, T., and Cicconi, P. (2021, January 9\u201310). A Methodological Proposal for the Comparison of 3D Photogrammetric Models. Proceedings of the Design Tools and Methods in Industrial Engineering II, Rome, Italy.","DOI":"10.1007\/978-3-030-91234-5"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jayathilakage, R., Rajeev, P., and Sanjayan, J. (2022). Rheometry for Concrete 3D Printing: A Review and an Experimental Comparison. Buildings, 12.","DOI":"10.3390\/buildings12081190"},{"key":"ref_4","unstructured":"The CGAL Project (2022). CGAL User and Reference Manual, CGAL Editorial Board. [5.4th ed.]."},{"key":"ref_5","unstructured":"Botsch, M., Steinberg, S., Bischoff, S., and Kobbelt, L. (2020, December 08). OpenMesh\u2014A Generic and Efficient Polygon Mesh Data Structure. Available online: https:\/\/www.graphics.rwth-aachen.de\/software\/openmesh\/."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fleishman, S., Drori, I., and Cohen-Or, D. (2003). Bilateral mesh denoising. ACM SIGGRAPH 2003 Papers, Association for Computing Machinery.","DOI":"10.1145\/1201775.882368"},{"key":"ref_7","unstructured":"Lee, K.W., and Wang, W.P. (2005, January 7\u201310). Feature-preserving mesh denoising via bilateral normal filtering. Proceedings of the Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG\u201905), Hong Kong, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hou, Q., Bai, L., and Wang, Y. (2005, January 22\u201325). Mesh smoothing via adaptive bilateral filtering. Proceedings of the International Conference on Computational Science, Atlanta, GA, USA.","DOI":"10.1007\/11428848_34"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ranjan, A., Bolkart, T., Sanyal, S., and Black, M.J. (2018, January 8\u201314). Generating 3D faces using Convolutional Mesh Autoencoders. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-01219-9_43"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lim, I., Dielen, A., Campen, M., and Kobbelt, L. (2018, January 8\u201314). A simple approach to intrinsic correspondence learning on unstructured 3D meshes. Proceedings of the European Conference on Computer Vision (ECCV) Workshops, Munich, Germany.","DOI":"10.1007\/978-3-030-11015-4_26"},{"key":"ref_11","unstructured":"Bouritsas, G., Bokhnyak, S., Ploumpis, S., Bronstein, M., and Zafeiriou, S. (November, January 27). Neural 3D morphable models: Spiral convolutional networks for 3D shape representation learning and generation. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Korea."},{"key":"ref_12","unstructured":"Gong, S., Chen, L., Bronstein, M., and Zafeiriou, S. (November, January 27). Spiralnet++: A fast and highly efficient mesh convolution operator. Proceedings of the IEEE\/CVF International Conference on Computer Vision Workshops, Seoul, Korea."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Verma, N., Boyer, E., and Verbeek, J. (2018, January 18\u201322). Feastnet: Feature-steered graph convolutions for 3D shape analysis. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00275"},{"key":"ref_14","first-page":"1397","article-title":"Learning Local Neighboring Structure for Robust 3D Shape Representation","volume":"35","author":"Gao","year":"2021","journal-title":"Proc. Aaai Conf. Artif. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2487228.2487237","article-title":"Screened poisson surface reconstruction","volume":"32","author":"Kazhdan","year":"2013","journal-title":"Acm Trans. Graph."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1007\/s00371-007-0167-y","article-title":"A robust hole-filling algorithm for triangular mesh","volume":"23","author":"Zhao","year":"2007","journal-title":"Vis. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Blanz, V., and Vetter, T. (1999, January 8\u201313). A morphable model for the synthesis of 3D faces. Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA.","DOI":"10.1145\/311535.311556"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Anguelov, D., Srinivasan, P., Koller, D., Thrun, S., Rodgers, J., and Davis, J. (2005). Scape: Shape completion and animation of people. ACM SIGGRAPH 2005 Papers, Association for Computing Machinery.","DOI":"10.1145\/1186822.1073207"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"194:1","DOI":"10.1145\/3130800.3130813","article-title":"Learning a model of facial shape and expression from 4D scans","volume":"36","author":"Li","year":"2017","journal-title":"ACM Trans. Graph."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"LeCun","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Azhar, I., Sharif, M., Raza, M., Khan, M.A., and Yong, H.S. (2021). A Decision Support System for Face Sketch Synthesis Using Deep Learning and Artificial Intelligence. Sensors, 21.","DOI":"10.3390\/s21248178"},{"key":"ref_22","unstructured":"Achlioptas, P., Diamanti, O., Mitliagkas, I., and Guibas, L. (2018, January 10\u201315). Learning representations and generative models for 3D point clouds. Proceedings of the International Conference on Machine Learning, PMLR, Stockholm, Sweden."},{"key":"ref_23","unstructured":"Qi, C.R., Su, H., Mo, K., and Guibas, L.J. (2017, January 21\u201326). Pointnet: Deep learning on point sets for 3D classification and segmentation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Su, H., Maji, S., Kalogerakis, E., and Learned-Miller, E. (2015, January 11\u201318). Multi-view convolutional neural networks for 3D shape recognition. Proceedings of the IEEE International conference on Computer Vision, Santiago, Chile.","DOI":"10.1109\/ICCV.2015.114"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wei, L., Huang, Q., Ceylan, D., Vouga, E., and Li, H. (2016, January 27\u201330). Dense human body correspondences using convolutional networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.171"},{"key":"ref_26","unstructured":"Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., and Xiao, J. (2015, January 7\u201312). 3D shapenets: A deep representation for volumetric shapes. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA."},{"key":"ref_27","first-page":"1","article-title":"Dynamic graph CNN for learning on point clouds","volume":"38","author":"Wang","year":"2019","journal-title":"Acm Trans. Graph."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MSP.2017.2693418","article-title":"Geometric deep learning: Going beyond Euclidean data","volume":"34","author":"Bronstein","year":"2017","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Choi, H., Moon, G., and Lee, K.M. (2020, January 23\u201328). Pose2mesh: Graph convolutional network for 3d human pose and mesh recovery from a 2d human pose. Proceedings of the European Conference on Computer Vision, Glasgow, UK.","DOI":"10.1007\/978-3-030-58571-6_45"},{"key":"ref_30","unstructured":"Apicella, A., Isgr\u00f2, F., Pollastro, A., and Prevete, R. (2021). Dynamic filters in graph convolutional neural networks. arXiv."},{"key":"ref_31","unstructured":"Bruna, J., Zaremba, W., Szlam, A., and LeCun, Y. (2013). Spectral networks and locally connected networks on graphs. arXiv."},{"key":"ref_32","first-page":"3844","article-title":"Convolutional neural networks on graphs with fast localized spectral filtering","volume":"29","author":"Defferrard","year":"2016","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Garland, M., and Heckbert, P.S. (1997, January 3\u20138). Surface simplification using quadric error metrics. Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA.","DOI":"10.1145\/258734.258849"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Litany, O., Bronstein, A., Bronstein, M., and Makadia, A. (2018, January 18\u201322). Deformable shape completion with graph convolutional autoencoders. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00202"},{"key":"ref_35","unstructured":"Kingma, D.P., and Welling, M. (2013). Auto-encoding variational bayes. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Dutilleux, P. (1990). An implementation of the \u201calgorithme \u00e0 trous\u201d to compute the wavelet transform. Wavelets, Springer.","DOI":"10.1007\/978-3-642-75988-8_29"},{"key":"ref_37","unstructured":"Liang-Chieh, C., Papandreou, G., Kokkinos, I., Murphy, K., and Yuille, A. (2015, January 7\u20139). Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs. Proceedings of the International Conference on Learning Representations, San Diego, CA, USA."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Gao, Z., Yan, J., Zhai, G., and Yang, X. (2021, January 19\u201327). Learning Spectral Dictionary for Local Representation of Mesh. Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI-21, Montreal, QC, Canada.","DOI":"10.24963\/ijcai.2021\/95"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Bogo, F., Romero, J., Pons-Moll, G., and Black, M.J. (2017, January 21\u201326). Dynamic FAUST: Registering Human Bodies in Motion. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.591"},{"key":"ref_40","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. Advances in Neural Information Processing Systems 32, Curran Associates, Inc."},{"key":"ref_41","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Mei, S., Liu, M., Kudreyko, A., Cattani, P., Baikov, D., and Villecco, F. (2022). Bendlet Transform Based Adaptive Denoising Method for Microsection Images. Entropy, 24.","DOI":"10.3390\/e24070869"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/17\/6457\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:16:21Z","timestamp":1760141781000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/17\/6457"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,27]]},"references-count":42,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22176457"],"URL":"https:\/\/doi.org\/10.3390\/s22176457","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,27]]}}}