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Abstract:
Intrinsic shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most
existing approaches assume global consistency. While global isometric
matching is well understood, only a few heuristic solutions are known
for partial matching. Partial matching is particularly important
for robustness to topological noise, which is a common problem in
real-world scanner data. We introduce a new approach to partial isometric
matching based on the observation that isometries are fully determined
by local information: a map of a single point and its tangent space
fixes an isometry. We develop a new representation for partial isometric
maps based on equivalence classes of correspondences between pairs
of points and their tangent-spaces. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods,
where we obtain significant improvements over global methods for
real-world data and stronger guarantees than previous partial matching
algorithms.
