Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit

by   Stefan C. Schonsheck, et al.

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us compute to geometric meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a 'target shape' and its deformed LB eigensytem. We solve the model using an proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a reinitialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noise on the underlying manifolds and errors within the given landmarks.


page 14

page 15

page 16


Shape analysis via inconsistent surface registration

In this work, we develop a framework for shape analysis using inconsiste...

Self-supervised Landmark Learning with Deformation Reconstruction and Cross-subject Consistency Objectives

A Point Distribution Model (PDM) is the basis of a Statistical Shape Mod...

Shape Analysis via Functional Map Construction and Bases Pursuit

We propose a method to simultaneously compute scalar basis functions wit...

Inconsistent Surface Registration via Optimization of Mapping Distortions

We address the problem of registering two surfaces, of which a natural b...

A novel variational model for image registration using Gaussian curvature

Image registration is one important task in many image processing applic...

How to Register a Live onto a Liver ? Partial Matching in the Space of Varifolds

Partial shapes correspondences is a problem that often occurs in compute...

Registration-free localization of defects in 3-D parts from mesh metrology data using functional maps

Spectral Laplacian methods, widely used in computer graphics and manifol...

Please sign up or login with your details

Forgot password? Click here to reset