  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.
