Non-isometric shape correspondence remains a fundamental challenge in
computer vision. Traditional methods using Laplace-Beltrami operator (LBO)
eigenmodes face limitations in characterizing high-frequency extrinsic shape
changes like bending and creases. We propose a novel approach of combining the
non-orthogonal extrinsic basis of eigenfunctions of the elastic thin-shell
hessian with the intrinsic ones of the LBO, creating a hybrid spectral space in
which we construct functional maps. To this end, we present a theoretical
framework to effectively integrate non-orthogonal basis functions into
descriptor- and learning-based functional map methods. Our approach can be
incorporated easily into existing functional map pipelines across varying
applications and is able to handle complex deformations beyond isometries. We
show extensive evaluations across various supervised and unsupervised settings
and demonstrate significant improvements. Notably, our approach achieves up to
15% better mean geodesic error for non-isometric correspondence settings and up
to 45% improvement in scenarios with topological noise.

非等距形状对应是计算机视觉中的一个基本挑战，本文提出了一种新方法，通过将弹性薄壳的非正交外部基函数与 Laplace-Beltrami 算子的内在基函数相结合，创建了一个混合谱空间来构建功能映射，实现了在各种应用中处理复杂变形的能力，并通过广泛的评估展示了显著的改进。