{"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/convolutional-neural-networks-on-non-uniform","title":"Convolutional Neural Networks on non-uniform geometrical signals using Euclidean spectral transformation","arxiv_id":"1901.02070","date":"2019-01-07","proceeding":"ICLR 2019 5","authors":["Chiyu \"Max\" Jiang","Dequan Wang","Jingwei Huang","Philip Marcus","Matthias Nießner"],"abstract":"Convolutional Neural Networks (CNN) have been successful in processing data\nsignals that are uniformly sampled in the spatial domain (e.g., images).\nHowever, most data signals do not natively exist on a grid, and in the process\nof being sampled onto a uniform physical grid suffer significant aliasing error\nand information loss. Moreover, signals can exist in different topological\nstructures as, for example, points, lines, surfaces and volumes. It has been\nchallenging to analyze signals with mixed topologies (for example, point cloud\nwith surface mesh). To this end, we develop mathematical formulations for\nNon-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample\nnonuniform data signals of different topologies defined on a simplex mesh into\nthe spectral domain with no spatial sampling error. The spectral transform is\nperformed in the Euclidean space, which removes the translation ambiguity from\nworks on the graph spectrum. Our representation has four distinct advantages:\n(1) the process causes no spatial sampling error during the initial sampling,\n(2) the generality of this approach provides a unified framework for using CNNs\nto analyze signals of mixed topologies, (3) it allows us to leverage\nstate-of-the-art backbone CNN architectures for effective learning without\nhaving to design a particular architecture for a particular data structure in\nan ad-hoc fashion, and (4) the representation allows weighted meshes where each\nelement has a different weight (i.e., texture) indicating local properties. We\nachieve results on par with the state-of-the-art for the 3D shape retrieval\ntask, and a new state-of-the-art for the point cloud to surface reconstruction\ntask.","url_abs":"http://arxiv.org/abs/1901.02070v1","url_pdf":"http://arxiv.org/pdf/1901.02070v1.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":"convolutional-neural-networks-on-non-uniform","repo_url":"https://github.com/clintonjwang/di-net","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"convolutional-neural-networks-on-non-uniform","repo_url":"https://github.com/maxjiang93/DDSL","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"3d-shape-retrieval","task_name":"3D Shape Classification"},{"task_slug":"3d-shape-retrieval-1","task_name":"3D Shape Retrieval"},{"task_slug":"retrieval","task_name":"Retrieval"},{"task_slug":"surface-reconstruction","task_name":"Surface Reconstruction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1901.02070","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}