Vector Field Map Representation for Near Conformal Surface Correspondence

Abstract

Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence. For function transfer between shapes, the preservation of function values on landmarks can be strictly enforced through our gradient domain representation, enabling transfer across different topologies. With the vector field map representation, a novel class of constraints can be specified for the alignment of designed or computed vector field pairs. We demonstrate the advantages of the vector field map representation in tests on conformal datasets and near‐isometric datasets.Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence.