The Quantile Matching Problem and Point Cloud Registration.

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2021 SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)The Quantile Matching Problem and Point Cloud RegistrationStéphane Chrétien, Oya Ekin Karaşan, Ecenur Oguz, and Mustafa Ç. PınarStéphane Chrétien, Oya Ekin Karaşan, Ecenur Oguz, and Mustafa Ç. Pınarpp.13 - 20Chapter DOI:https://doi.org/10.1137/1.9781611976830.2PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract One of the fundamental problems in computer vision is the matching of two point clouds. For the case when the two point clouds do not match exactly we introduce a new approach based on quantile matching using curvature information. We define the quantile matching problem on a bipartite graph, the two parts of which represent two point clouds. The goal is to achieve an optimal registration of a point cloud with another point cloud. The problem is posed as the problem of computing a (perfect when possible) matching, which maximizes the α-quantile of affinity weights between the nodes of the graph. We prove that the problem is polynomially solvable in bipartite and non-bipartite graphs. Numerical illustrations are given. Implementations of the proposed algorithms in Python are described along with computational results with synthetic as well as real data from an optical coherence tomography application. Previous chapter Next chapter RelatedDetails Published:2021eISBN:978-1-61197-683-0 https://doi.org/10.1137/1.9781611976830Book Series Name:ProceedingsBook Code:PRACDA21Book Pages:1-239