  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.
