2023/03/27 by Daniel Widdowson, Widdowson, Daniel, Vitaliy Kurlin +1 · 3 citations
Computer Science · Engineering · Environmental Science · #3D Shape Modeling and Analysis #51F20 #51F30 #51K05 #51N20 #68U05 #Computational Geometry (cs.CG) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #I.5.1 #I.5.2 #Image Processing and 3D Reconstruction #Metric Geometry (math.MG) #Remote Sensing and LiDAR Applications
paper · pdf · doi:10.48550/arxiv.2303.15385
openalex publication_date 2023/03/27 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description). Noise and motion in data motivate a search for invariants that are continuous under perturbations of points in a suitable metric. We propose the first continuous and complete invariant of unlabeled clouds in any Euclidean space. For a fixed dimension, the new metric for this invariant is computable in a polynomial time in the number of points.