Stable Geodesic Surface Signatures

Shape analysis plays a fundamental role in computer graphics. We present a novel global and intrinsic shape representation for shape analysis, called stable geodesic signature. It is based on the theory of stable closed geodesics and surface Ricci flow. We examine the surface by dynamically deforming it by metric design through Ricci flow, then we observe the behavior of the stable closed geodesics under the evolving Riemannian metrics. When a metric is deforming, some stable geodesic loops will become unstable and shrink to points, or some geodesic loops may merge. The number of stable geodesics forms the signature, which is general for arbitrary surfaces. Experiments on a large amount of surfaces demonstrate the efficiency and efficacy of the stable geodesic signature for shape analysis.