Conformal geometric methods in computer vision

Shape analysis has fundamental importance in computer vision, including surface matching, registration, tracking, classification, recognition, etc. Computational methods based on conformal geometry can map any 3D surface to a 2D canonical domain. They provide a novel approach to 3D problems by converting them to 2D problems, which greatly simplifies the computation process. With this framework, we present a series of matching and registration methods for general surfaces, especially with large non-rigid deformations and complicated topologies. In addition, we introduce a global and unique shape signature for shape recognition applications. Experiments on a variety of real scans from different equipments demonstrate the efficiency and efficacy of the conformal geometric methods in computer vision applications.