Elastic Correspondence between Triangle Meshes

We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non-linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non-isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non-isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross-field computation, and consistent quadrangular remeshing of a set of shapes.D. Ezuz acknowledges funding from the Irwin and Joan Jacobs fellowship. B. Heeren and M. Rumpf acknowledge the support of the Hausdorff Center for Mathematics. B. Heeren M. Rumpf and M. Ben Chen acknowledge the support by a grant from the GIF, the German-Israeli Foundation for Scientific Research and Development (grant number I-1339-407.6/2016). O. Azencot acknowledges the support by a Zuckerman STEM Leadership Postdoctoral Fellowship. M. Ben Chen acknowledges the support of the Israel Science Foundation (grant No. 504/16)