Point-wise Map Recovery and Refinement from Functional Correspondence
This addresses a key bottleneck in shape analysis for researchers and practitioners, enabling more robust correspondence recovery beyond near-isometric assumptions.
The paper tackles the problem of converting functional maps back to point-to-point maps, which is crucial for shape analysis applications, and achieves remarkable accuracy improvements in challenging cases.
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape matching and image segmentation, to exploration of large shape collections. Despite the numerous advantages of such representation, however, the problem of converting a given functional map back to a point-to-point map has received a surprisingly limited interest. In this paper we analyze the general problem of point-wise map recovery from arbitrary functional maps. In doing so, we rule out many of the assumptions required by the currently established approach -- most notably, the limiting requirement of the input shapes being nearly-isometric. We devise an efficient recovery process based on a simple probabilistic model. Experiments confirm that this approach achieves remarkable accuracy improvements in very challenging cases.