{"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/monte-carlo-convolution-for-learning-on-non","title":"Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds","arxiv_id":"1806.01759","date":"2018-06-05","proceeding":null,"authors":["Pedro Hermosilla","Tobias Ritschel","Pere-Pau Vázquez","Àlvar Vinacua","Timo Ropinski"],"abstract":"Deep learning systems extensively use convolution operations to process input\ndata. Though convolution is clearly defined for structured data such as 2D\nimages or 3D volumes, this is not true for other data types such as sparse\npoint clouds. Previous techniques have developed approximations to convolutions\nfor restricted conditions. Unfortunately, their applicability is limited and\ncannot be used for general point clouds. We propose an efficient and effective\nmethod to learn convolutions for non-uniformly sampled point clouds, as they\nare obtained with modern acquisition techniques. Learning is enabled by four\nkey novelties: first, representing the convolution kernel itself as a\nmultilayer perceptron; second, phrasing convolution as a Monte Carlo\nintegration problem, third, using this notion to combine information from\nmultiple samplings at different levels; and fourth using Poisson disk sampling\nas a scalable means of hierarchical point cloud learning. The key idea across\nall these contributions is to guarantee adequate consideration of the\nunderlying non-uniform sample distribution function from a Monte Carlo\nperspective. To make the proposed concepts applicable to real-world tasks, we\nfurthermore propose an efficient implementation which significantly reduces the\nGPU memory required during the training process. By employing our method in\nhierarchical network architectures we can outperform most of the\nstate-of-the-art networks on established point cloud segmentation,\nclassification and normal estimation benchmarks. Furthermore, in contrast to\nmost existing approaches, we also demonstrate the robustness of our method with\nrespect to sampling variations, even when training with uniformly sampled data\nonly. To support the direct application of these concepts, we provide a\nready-to-use TensorFlow implementation of these layers at\nhttps://github.com/viscom-ulm/MCCNN","url_abs":"http://arxiv.org/abs/1806.01759v2","url_pdf":"http://arxiv.org/pdf/1806.01759v2.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":"monte-carlo-convolution-for-learning-on-non","repo_url":"https://github.com/viscom-ulm/MCCNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":null,"task_name":"GPU"},{"task_slug":"point-cloud-segmentation","task_name":"Point Cloud Segmentation"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1806.01759","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}