Volume 55, Number 3, May-June 2021
|Page(s)||1133 - 1161|
|Published online||08 June 2021|
Symmetry and scaling limits for matching of implicit surfaces based on thin shell energies
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria
* Corresponding author: email@example.com
Accepted: 11 April 2021
In a recent paper by Iglesias et al. [Found. Comput. Math. 18 (2018) 891–927] a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic energies active only in a narrow band around the hypersurfaces that resemble the behavior of elastic shells. In this work we consider some extensions and further analysis of that model. First, we present a symmetric energy functional such that given two particular shapes, it assigns the same energy to any given deformation as to its inverse when the roles of the shapes are interchanged, and introduce the adequate parameter scaling to recover a surface problem when the width of the narrow band vanishes. Then, we obtain existence of minimizing deformations for the symmetric energy in classes of bi-Sobolev homeomorphisms for small enough widths, and prove a Γ-convergence result for the corresponding non-symmetric energies as the width tends to zero. Finally, numerical results on realistic shape matching applications demonstrating the effect of the symmetric energy are presented.
Mathematics Subject Classification: 49J45 / 65D18 / 74K25
Key words: Variational shape matching / implicit surfaces / thin shells / invertibility / scaling limits
© EDP Sciences, SMAI 2021
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