Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics A Comprehensive Numerical Framework
CC BY
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s11263-022-01743-0 https://dlib.phenikaa-uni.edu.vn/handle/PNK/8275 |
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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 |
8.887836 |