A Thin Shell Approach to the Registration of Implicit Surfaces

Iglesias, Jose A.; Berkels, Benjamin; Rumpf, Martin; Scherzer, Otmar

A Thin Shell Approach to the Registration of Implicit Surfaces

Files

089-096.pdf (6.19 MB)

Date

2013

Authors

Iglesias, Jose A.
Berkels, Benjamin
Rumpf, Martin
Scherzer, Otmar

Publisher

The Eurographics Association

Abstract

Frequently, one aims at the co-registration of geometries described implicitly by images as level sets. This paper proposes a novel shape sensitive approach for the matching of such implicit surfaces. Motivated by physical models of elastic shells a variational approach is proposed, which distinguishes two different types of energy contributions: a membrane energy measuring the rate of tangential distortion when deforming the reference surface into the template surface, and a bending energy reflecting the required amount of bending. The variational model is formulated via a narrow band approach. The built in tangential distortion energy leads to a suitable equidistribution of deformed length and area elements, under the optimal matching deformation, whereas the minimization of the bending energy fosters a proper matching of shape features such as crests, valleys or bumps. In the implementation, a spatial discretization via finite elements, a nonlinear conjugate gradient scheme with a Sobolev metric, and a cascadic multilevel optimization strategy are used. The features of the proposed method are discussed via applications both for synthetic and realistic examples.

        @inproceedings{:10.2312/PE.VMV.VMV13.089-096
,
booktitle = {Vision, Modeling & Visualization
},
editor = {Michael Bronstein and Jean Favre and Kai Hormann
},
title = {{A Thin Shell Approach to the Registration of Implicit Surfaces
}},
author = {Iglesias, Jose A. and 
Berkels, Benjamin and 
Rumpf, Martin and 
Scherzer, Otmar
},
year = {2013
},
publisher = {The Eurographics Association
},
ISBN = {978-3-905674-51-4
},
DOI = {/10.2312/PE.VMV.VMV13.089-096
}
}