Continuous Matching via Vector Field Flow

We present a new method for non-rigid shape matching designed to enforce continuity of the resulting correspondence. Our method is based on the recently proposed functional map representation, which allows efficient manipulation and inference but often fails to provide a continuous point-to-point mapping. We address this problem by exploiting the connection between the operator representation of mappings and flows of vector fields. In particular, starting from an arbitrary continuous map between two surfaces we find an optimal flow that makes the final correspondence operator as close as possible to the initial functional map. Our method also helps to address the symmetric ambiguity problem inherent in many intrinsic correspondence methods when matching symmetric shapes. We provide practical and theoretical results showing that our method can be used to obtain an orientation preserving or reversing map starting from a functional map that represents the mixture of the two. We also show how this method can be used to improve the quality of maps produced by existing shape matching methods, and compare the resulting map's continuity with results obtained by other operator-based techniques.