{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/polynet-polynomial-neural-network-for-3d","title":"PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representation","arxiv_id":"2110.07882","date":"2021-10-15","proceeding":null,"authors":["Mohsen Yavartanoo","Shih-Hsuan Hung","Reyhaneh Neshatavar","Yue Zhang","Kyoung Mu Lee"],"abstract":"3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some challenges for the existing deep neural network (DNN)-based methods on polygon mesh representation, such as handling the variations in the degree and permutations of the vertices and their pairwise distances. To overcome these challenges, we propose a DNN-based method (PolyNet) and a specific polygon mesh representation (PolyShape) with a multi-resolution structure. PolyNet contains two operations; (1) a polynomial convolution (PolyConv) operation with learnable coefficients, which learns continuous distributions as the convolutional filters to share the weights across different vertices, and (2) a polygonal pooling (PolyPool) procedure by utilizing the multi-resolution structure of PolyShape to aggregate the features in a much lower dimension. Our experiments demonstrate the strength and the advantages of PolyNet on both 3D shape classification and retrieval tasks compared to existing polygon mesh-based methods and its superiority in classifying graph representations of images. The code is publicly available from https://myavartanoo.github.io/polynet/.","url_abs":"https://arxiv.org/abs/2110.07882v1","url_pdf":"https://arxiv.org/pdf/2110.07882v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"polynet-polynomial-neural-network-for-3d","repo_url":"https://github.com/myavartanoo/PolyNet_PyTorch","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"3d-object-classification","task_name":"3D Object Classification"},{"task_slug":"3d-point-cloud-classification","task_name":"3D Point Cloud Classification"},{"task_slug":"3d-shape-retrieval","task_name":"3D Shape Classification"},{"task_slug":"3d-shape-recognition","task_name":"3D Shape Recognition"},{"task_slug":"3d-shape-representation","task_name":"3D Shape Representation"},{"task_slug":"retrieval","task_name":"Retrieval"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"polyconv","method_name":"PolyConv"}],"datasets_introduced":[],"methods_introduced":[{"slug":"polyconv","name":"PolyConv","full_name":"Polynomial Convolution"}],"results":[{"leaderboard":"/sota/3d-object-classification-on-modelnet10","task":"3D Object Classification","dataset":"ModelNet10","model":"PolyNet","rank_in_archive_order":1,"of":4,"metrics":{"Accuracy":"94.93"},"uses_additional_data":false},{"leaderboard":"/sota/3d-point-cloud-classification-on-modelnet40","task":"3D Point Cloud Classification","dataset":"ModelNet40","model":"PolyNet","rank_in_archive_order":88,"of":111,"metrics":{"Overall Accuracy":"92.42"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}