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.

本文提出了一种方法，利用函数映射框架高效计算非刚性形状之间具有保方向和近似连续性的对应关系，并通过引入新的方法对初始函数映射进行改进，从而获得高质量的点对应关系。研究表明，该方法在保持连续性和覆盖率方面显著优于现有技术，并且产生的对应关系是有意义的。