||Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a
surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching
point set surfaces, which is invariant with respect to isometries. A set of reference points, evenly distributed on
the point set surface, is sampled by farthest point sampling. The geodesic distance between reference points is
normalized and stored in a geodesic distance matrix. Each row of the matrix yields a histogram of its elements.
The set of histograms of the rows of a distance matrix is taken as a descriptor of the shape of the surface. The
dissimilarity between two point set surfaces is computed by matching the corresponding sets of histograms with
bipartite graph matching. This is an effective method for classifying and recognizing objects deformed with
isometric transformations, e.g., non-rigid and articulated objects in different postures.