Learning from landmarks, curves, surfaces, and shapes in Geomstats
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arXiv
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| Autores principales: | , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929393116381184 |
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| author | Pereira, Luís F. Brigant, Alice Le Myers, Adele Hartman, Emmanuel Khan, Amil Tuerkoen, Malik Dold, Trey Gu, Mengyang Suárez-Serrato, Pablo Miolane, Nina |
| author_facet | Pereira, Luís F. Brigant, Alice Le Myers, Adele Hartman, Emmanuel Khan, Amil Tuerkoen, Malik Dold, Trey Gu, Mengyang Suárez-Serrato, Pablo Miolane, Nina |
| contents | We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The shape module further implements the abstract mathematical structures of group actions, fiber bundles, quotient spaces and associated Riemannian metrics which allow users to build their own shape spaces. The Riemannian geometry tools enable users to compare, average, interpolate between shapes inside a given shape space. These essential operations can then be leveraged to perform statistics and machine learning on shape data. We present the object-oriented implementation of the shape module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning from landmarks, curves, surfaces, and shapes in Geomstats Pereira, Luís F. Brigant, Alice Le Myers, Adele Hartman, Emmanuel Khan, Amil Tuerkoen, Malik Dold, Trey Gu, Mengyang Suárez-Serrato, Pablo Miolane, Nina Graphics Mathematical Software Differential Geometry We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The shape module further implements the abstract mathematical structures of group actions, fiber bundles, quotient spaces and associated Riemannian metrics which allow users to build their own shape spaces. The Riemannian geometry tools enable users to compare, average, interpolate between shapes inside a given shape space. These essential operations can then be leveraged to perform statistics and machine learning on shape data. We present the object-oriented implementation of the shape module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces. |
| title | Learning from landmarks, curves, surfaces, and shapes in Geomstats |
| topic | Graphics Mathematical Software Differential Geometry |
| url | https://arxiv.org/abs/2406.10437 |