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Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework

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Bibliographic Details
Main Authors: Emmanuel, Hartman, Yashil, Sukurdeep, Eric, Klassen
Format: Book
Language:English
Published: Springer 2023
Subjects:
Elastic Shape Analysis
Online Access:https://link.springer.com/article/10.1007/s11263-022-01743-0
https://dlib.phenikaa-uni.edu.vn/handle/PNK/8275
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spelling oai:localhost:PNK-82752023-04-25T04:56:48Z Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework Emmanuel, Hartman Yashil, Sukurdeep Eric, Klassen Elastic Shape Analysis CC BY This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic distances between parametrized or unparametrized immersed surfaces represented as 3D meshes. Building on this, we develop tools for the statistical shape analysis of sets of surfaces, including methods for estimating Karcher means and performing tangent PCA on shape populations, and for computing parallel transport along paths of surfaces. Our proposed approach fundamentally relies on a relaxed variational formulation for the geodesic matching problem via the use of varifold fidelity terms, which enable us to enforce reparametrization independence when computing geodesics between unparametrized surfaces, while also yielding versatile algorithms that allow us to compare surfaces with varying sampling or mesh structures. 2023-04-25T04:56:48Z 2023-04-25T04:56:48Z 2023 Book https://link.springer.com/article/10.1007/s11263-022-01743-0 https://dlib.phenikaa-uni.edu.vn/handle/PNK/8275 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic Elastic Shape Analysis
spellingShingle Elastic Shape Analysis
Emmanuel, Hartman
Yashil, Sukurdeep
Eric, Klassen
Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
description CC BY
format Book
author Emmanuel, Hartman
Yashil, Sukurdeep
Eric, Klassen
author_facet Emmanuel, Hartman
Yashil, Sukurdeep
Eric, Klassen
author_sort Emmanuel, Hartman
title Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
title_short Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
title_full Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
title_fullStr Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
title_full_unstemmed Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
title_sort elastic shape analysis of surfaces with second-order sobolev metrics a comprehensive numerical framework
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s11263-022-01743-0
https://dlib.phenikaa-uni.edu.vn/handle/PNK/8275
_version_ 1764177437112926208
score 8.891145

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