Geodesic Mapping for Dynamic Surface Alignment

Tony Tung, Takashi Matsuyama

Abstract: This paper presents a novel approach that achieves dynamic surface alignment by geodesing mapping. The surfaces are 3D manifold meshes representing non-rigid objects in motion (e.g., humans) which can be obtained by multiview stereo reconstruction. The proposed framework consists of a geodesic mapping (i.e., geodesic diffeomorphism) between surfaces which carry a distance function (namely the global geodesic distance), and a geodesic-based coordinate system (namely the global geodesic coordinates) defined similarly to generalized barycentric coordinates. The coordinates are used to recursively choose correspondence points in non-ambiguous regions using a coarse-to-fine strategy to reliably locate all surface points and define a discrete mapping. Complete point-to-point surface alignment with smooth mapping is then derived by optimizing a piecewise objective function within a probabilistic framework. The proposed technique only relies on surface intrinsic geometrical properties, and does not require prior knowledge on surface appearance (e.g., color or texture), shape (e.g., topology) or parameterization (e.g., mesh connectivity or complexity). The method can be used for numerous applications, such as visual information (e.g., texture) transfer between surface models representing different objects, dense motion flow estimation of 3D dynamic surfaces, wide-timeframe matching, etc. Experiments show compelling results on challenging publicly available real-world datasets.