Shape correspondences: Local to global

Finding correspondences between two or more shapes is a fundamental and still unsolved problem in computer graphics and computer vision. Typically, one is interested in finding correspondence between similar objects (e.g. shapes representing different four-legged animals) or deformed versions of the same object (e.g. model of a human in different poses). The problem often suffers from ambiguities, which are brought about by shape symmetry, point slippage, edge stretching and shrinking. Most approaches to shape correspondence put restrictions on the deformation model: for example, matching techniques tailored for near isometric, area preserving or articulated deformations have been developed. Ideally, one would like to design an optimization based approach that would produce an optimal correspondence subject to constraints on the deformation model. However, setting up an optimization problem that can reliably provide a high quality solution and, at the same time, is computationally tractable, has been a major challenge. The correspondence problem solutions are often broken into three stages: 1. extract salient features in the input shapes; 2. perform rough matching of the salient features using descriptors; 3. globally register two shapes based on the rough matching.;We propose several new contributions to different stages of this framework.;First, we design a local shape descriptor based on the classical Spin Image. Our descriptor Spin Contour is essentially the contour of the original Spin Image. It provides considerably higher quality matching results while making comparisons between the descriptors more efficient.;Second, we introduce the Geodesic Spin Contour, a variant of the Spin Contour suitable for non-rigid near-isometric shape matching by replacing the Euclidean-based spin coordinates with geodesic-based coordinates. This descriptor compares favorably with state-of-the-art local shape descriptors when for matching shapes deformed in a near-isometric manner. The Geodesic Spin Contour is suitable for partial matching, i.e. matching shapes with missing parts.;Third, we develop a fully automatic surface registration scheme. This method matches near-isometric shapes by globally minimizing the geodesic distance differences between pairs of features.;Finally, we extend the Iterative Closest Point (ICP) scheme to nonrigid non-isometric registration. Instead of using 1-1 mapping, we use many-many mapping to recover the nontrivial underlying deformation.