Surface Shape Matching and Analysis using Intrinsic Coordinate Parameterizations

This paper presents a geometric method for parameterization, matching, and analysis of surface shapes. Surfaces are parameterized and represented by intrinsic coordinate maps derived from the conformal structure of the shape. This parameterization is invariant to rigid transformations of the shape, as well as angle-preserving parameterizations of the surface. Shape matching between coordinate maps of two surfaces is achieved by i) deforming the isothermal curves of the intrinsic parameterization under a nonlinear transformation, and ii) locally reparameterizing the isothermal curves to yield invariant diffeomorphic matchings. Experimental results are shown in synthetic data as well as neuroanatomical shapes such as the hippocampus and the cortex.