A New Riemannian Setting for Surface Registration

2011/06/03 by Martin Bauer, Bauer, Martin, Martins Bruveris +1 · 3 citations
Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Morphological variations and asymmetry #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1106.0620

openalex publication_date 2011/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latter approach a deformation is prescribed on the ambient space, which then drags along an embedded surface. In contrast our metric is defined directly on the deformation vector field and can therefore be called an inner metric. We also show how to discretize the corresponding geodesic equation and compute the gradient of the cost functional using finite elements.

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• Discrete geodesic calculus in the space of viscous fluidic objects
• Isometry‐Aware Preconditioning for Mesh Parameterization
• Fracture propagation by using shape optimization techniques based on outer Riemannian metrics

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