The Quantile Matching Problem and Point Cloud Registration
Stéphane Chrétien, Oya Ekin Karaşan, Ecenur Oğuz, Mustafa Çelebi Pınar · Society for Industrial and Applied Mathematics eBooks · 2021
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.