Gaussian-curvature-derived invariants for isometry

Surface deformations without tearing or stretching, preserving the intrinsic properties, are called isometries. This paper presents a new definition of Gaussian curvature moments (GCMs) by the integral of n power of Gaussian curvature. Then a series of moment invariants, called Gaussian curvature moment invariants (GCMIs), are derived via GCMs. These moment invariants share many good properties under rigid transformations and isometric non-rigid transformations, and Gaussian-Bonnet theorem is a special case of GCMI. GCMIs are invariant under isometry and scaling transformations. We construct an invariant vector as a descriptor for a surface via GCMIs, and a modified χ2 distance is defined as a measure of similarity. Finally, experiments show that it is a reliable descriptor for isometric non-rigid shape.