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Softw."],"published-print":{"date-parts":[[2026,3,31]]},"abstract":"<jats:p>\n                    We introduce the\n                    <jats:monospace>shape<\/jats:monospace>\n                    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\n                    <jats:monospace>shape<\/jats:monospace>\n                    module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The\n                    <jats:monospace>shape<\/jats:monospace>\n                    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\n                    <jats:monospace>shape<\/jats:monospace>\n                    module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces.\n                  <\/jats:p>","DOI":"10.1145\/3779118","type":"journal-article","created":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T03:00:31Z","timestamp":1765508431000},"page":"1-31","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Learning from Landmarks, Curves, Surfaces, and Shapes in Geomstats"],"prefix":"10.1145","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3017-9553","authenticated-orcid":false,"given":"Lu\u00eds F.","family":"Pereira","sequence":"first","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA, Universit\u00e0 degli Studi di Milano-Bicocca, Milano, Italy, and Inria Center at Universit\u00e9 C\u00f4te d\u2019Azur, Valbonne, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8055-4753","authenticated-orcid":false,"given":"Alice Le","family":"Brigant","sequence":"additional","affiliation":[{"name":"University Paris 1 Panth\u00e9on-Sorbonne, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6887-1820","authenticated-orcid":false,"given":"Adele","family":"Myers","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5754-2930","authenticated-orcid":false,"given":"Emmanuel","family":"Hartman","sequence":"additional","affiliation":[{"name":"University of Houston, Houston, Texas, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1153-7703","authenticated-orcid":false,"given":"Amil","family":"Khan","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3268-7903","authenticated-orcid":false,"given":"Malik","family":"Tuerkoen","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4264-6069","authenticated-orcid":false,"given":"Trey","family":"Dold","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3959-8965","authenticated-orcid":false,"given":"Mengyang","family":"Gu","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1138-0921","authenticated-orcid":false,"given":"Pablo","family":"Su\u00e1rez-Serrato","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1ticas UNAM, Mexico DF, Mexico and Max Planck Institute for Mathematics, Bonn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1200-9024","authenticated-orcid":false,"given":"Nina","family":"Miolane","sequence":"additional","affiliation":[{"name":"University of California Santa Barbara, Santa Barbara, California, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2026,3,17]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1066282"},{"key":"e_1_3_2_3_1","doi-asserted-by":"crossref","unstructured":"Martin Bauer Martins Bruveris Nicolas Charon and Jakob M\u00f8ller-Andersen. 2018. 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