Comparing point clouds
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, page 32--40. ACM, (2004)Abstract
Point clouds are one of the most primitive and fundamental surface representations. A popular source of point
clouds are three dimensional shape acquisition devices such as laser range scanners. Another important field
where point clouds are found is in the representation of high-dimensional manifolds by samples. With the increas-
ing popularity and very broad applications of this source of data, it is natural and important to work directly
with this representation, without having to go to the intermediate and sometimes impossible and distorting steps
of surface reconstruction. A geometric framework for comparing manifolds given by point clouds is presented
in this paper. The underlying theory is based on Gromov-Hausdorff distances, leading to isometry invariant and
completely geometric comparisons. This theory is embedded in a probabilistic setting as derived from random
sampling of manifolds, and then combined with results on matrices of pairwise geodesic distances to lead to a
computational implementation of the framework. The theoretical and computational results here presented are
complemented with experiments for real three dimensional shapes.