Structured Regularization of Functional Map Computations

09/30/2020
by   Jing Ren, et al.
0

We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace-Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well-justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one-parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly-used refinement techniques.

READ FULL TEXT
04/16/2019

ZoomOut: Spectral Upsampling for Efficient Shape Correspondence

We present a simple and efficient method for refining maps or correspond...
06/18/2015

Point-wise Map Recovery and Refinement from Functional Correspondence

Since their introduction in the shape analysis community, functional map...
10/06/2021

Learning Canonical Embedding for Non-rigid Shape Matching

This paper provides a novel framework that learns canonical embeddings f...
12/05/2021

Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud

Despite the success of deep functional maps in non-rigid 3D shape matchi...
04/24/2019

OperatorNet: Recovering 3D Shapes From Difference Operators

This paper proposes a learning-based framework for reconstructing 3D sha...
05/29/2019

Smooth Shells: Multi-Scale Shape Registration with Functional Maps

We propose a novel 3D shape correspondence method based on the iterative...
09/28/2018

Functional Maps Representation on Product Manifolds

We consider the tasks of representing, analyzing and manipulating maps b...