Paper Info
Title
Nonisometric Surface Registration Via Conformal Laplace-Beltrami Basis Pursuit
Abstract
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 to compute geometrically 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 eigensystem. We solve the model using a proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a re-initialization 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 noises on the underlying manifolds and errors within the given landmarks or feature functions.
Year
DOI
Venue
2018
10.1007/s10915-020-01390-y
JOURNAL OF SCIENTIFIC COMPUTING
Keywords
Field
DocType
Shape analysis, Laplace-Beltrami eigensystem, Conformal deformation, Nonisometric manifold matching
Laplace transform,Geometry processing,Mathematical analysis,Basis pursuit,Algorithm,Robustness (computer science),Conformal map,Augmented Lagrangian method,Landmark,Manifold,Mathematics
Journal
Volume
Issue
ISSN
86
3
0885-7474
Citations 
PageRank 
References 
1
0.35
20
Authors
3
Name
Order
Citations
PageRank
Stefan C. Schonsheck110.69
Michael M. Bronstein210.35
Rongjie Lai323919.84