Size and shape comparisons from noisy, unlabeled, incomplete configurations of landmarks in three-dimensional space

Document Type

Conference Paper/Presentation

Publication Date



This report discusses the size and shape comparison of objects represented by two sets of three dimensional data. We examine geometric invariants such as pairwise distances, distances from the centroid, and the volumes of the tetrahedrons. We examine rigid motion estimation using Procrustes analysis, the iterative closest point algorithm, and various uses of invariants. Using distance matrices, we develop a method to solve for point correspondences, and demonstrate its robustness to noise in the point coordinates. We also develop a method to find an isometric image of a small subset within a large set using pairwise distances and edge connectivity.

Publisher's Statement

© 2007 Institute for Mathematics and its Applications, University of Minnesota.

Publication Title

Mathematical Modeling in Industry XI - A Workshop for Graduate Students