# Shape Aware Matching of Implicit Surfaces based on Thin Shell Energies

arXiv: https://arxiv.org/abs/1509.06559 · HTML: https://mlsanity.com/paper/1509.06559/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2015.

## Built on by (most cited first, 4 of 4)

- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching](https://mlsanity.com/paper/2211.14604/) (2022)
- [Image comparison and scaling via nonlinear elasticity](https://mlsanity.com/paper/2303.10103/) (2023)
- [A nonlinear elasticity model in computer vision](https://mlsanity.com/paper/2408.17237/) (2024)

## Abstract (arXiv)

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.