. Given a pair of shapes, our method produces a point-wise map that is orientation-preserving as well as approximately continuous and bijective. Here we show the maps produced by different methods via texture transfer: BIM [Kim et al. 2011 ] has a large distortion on the face and the left hand; functional maps with ICP [Ovsjanikov et al. 2012] and PMF with the Gauss kernel [Vestner et al. 2017b] give a map that is flipped left to right; for PMF with the heat kernel [Vestner et al. 2017a] , the orientation in the torso region is reversed; The map produced by our method preserves the orientation consistently and has lower overall error when compared to the ground-truth. We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information. This allows us to obtain functional maps that promote orientation preservation, even when using descriptors, that are invariant to orientation changes. We then show how higher quality, approximately continuous and bijective pointwise correspondences can be obtained from initial functional maps by introducing a novel refinement technique that aims to simultaneously improve the maps both in the spectral and spatial domains. This leads to a general pipeline for computing correspondences between shapes that results in high-quality maps, while admitting an efficient optimization scheme. We show through extensive evaluation that our approach improves upon state-of-the-art results on challenging isometric and non-isometric correspondence benchmarks according to both measures of continuity and coverage as well as producing semantically meaningful correspondences as measured by the distance to ground truth maps.
Finally, REF iteratively alternate between improving the map in its spectral and spatial domains.
Continuous and Orientation-preserving Correspondences via Functional Maps
SIGGRAPH Asia '18
Computer Science Mathematics