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In this paper, we study the point cloud density adaptation problem that underlies many pre\u2010processing tasks of points data. Specifically, given a (sparse) set of points <jats:italic>Q<\/jats:italic> sampling an unknown surface and a target density function, the goal is to adapt <jats:italic>Q<\/jats:italic> to match the target distribution. We propose a simple and robust framework that is effective at achieving both local uniformity and precise global density distribution control. Our approach relies on the Gaussian\u2010weighted graph Laplacian and works purely in the points setting. While it is well known that graph Laplacian is related to mean\u2010curvature flow and thus has denoising ability, our algorithm uses certain information encoded in the graph Laplacian that is orthogonal to the mean\u2010curvature flow. Furthermore, by leveraging the natural scale parameter contained in the Gaussian kernel and combining it with a simulated annealing idea, our algorithm moves points in a multi\u2010scale manner. The resulting algorithm relies much less on the input points to have a good initial distribution (neither uniform nor close to the target density distribution) than many previous refinement\u2010based methods. We demonstrate the simplicity and effectiveness of our algorithm with point clouds sampled from different underlying surfaces with various geometric and topological properties.<\/jats:p>","DOI":"10.1111\/cgf.13293","type":"journal-article","created":{"date-parts":[[2017,9,14]],"date-time":"2017-09-14T16:18:43Z","timestamp":1505405923000},"page":"325-337","update-policy":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian"],"prefix":"10.1111","volume":"37","author":[{"given":"Chuanjiang","family":"Luo","sequence":"first","affiliation":[{"name":"The Ohio State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyin","family":"Ge","sequence":"additional","affiliation":[{"name":"The Ohio State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yusu","family":"Wang","sequence":"additional","affiliation":[{"name":"The Ohio State University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2017,9,14]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2003.1175093"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015713"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/0216006"},{"key":"e_1_2_7_5_1","unstructured":"[Bel03]\u00a0BelkinM.:Problems of Learning on Manifolds. 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