{"title":"Affine-invariant geodesic geometry of deformable 3D shapes","abstract":[{"text":"Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in \r\n in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.","lang":"eng"}],"scopus_import":"1","publication_status":"published","arxiv":1,"page":"692-697","publication":"Computers & Graphics","status":"public","external_id":{"arxiv":["1012.5936"]},"publication_identifier":{"issn":["0097-8493"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Raviv","full_name":"Raviv, Dan","first_name":"Dan"},{"orcid":"0000-0001-9699-8730","full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","last_name":"Bronstein","first_name":"Alexander"},{"last_name":"Bronstein","full_name":"Bronstein, Michael M.","first_name":"Michael M."},{"first_name":"Ron","full_name":"Kimmel, Ron","last_name":"Kimmel"},{"first_name":"Nir","full_name":"Sochen, Nir","last_name":"Sochen"}],"day":"01","publisher":"Elsevier","extern":"1","oa_version":"Preprint","issue":"3","OA_type":"green","date_created":"2024-10-15T11:20:54Z","year":"2011","date_updated":"2024-11-12T08:37:24Z","volume":35,"article_type":"letter_note","type":"journal_article","month":"06","language":[{"iso":"eng"}],"_id":"18363","doi":"10.1016/j.cag.2011.03.030","date_published":"2011-06-01T00:00:00Z","intvolume":"        35","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1012.5936"}],"citation":{"mla":"Raviv, Dan, et al. “Affine-Invariant Geodesic Geometry of Deformable 3D Shapes.” <i>Computers &#38; Graphics</i>, vol. 35, no. 3, Elsevier, 2011, pp. 692–97, doi:<a href=\"https://doi.org/10.1016/j.cag.2011.03.030\">10.1016/j.cag.2011.03.030</a>.","chicago":"Raviv, Dan, Alex M. Bronstein, Michael M. Bronstein, Ron Kimmel, and Nir Sochen. “Affine-Invariant Geodesic Geometry of Deformable 3D Shapes.” <i>Computers &#38; Graphics</i>. Elsevier, 2011. <a href=\"https://doi.org/10.1016/j.cag.2011.03.030\">https://doi.org/10.1016/j.cag.2011.03.030</a>.","short":"D. Raviv, A.M. Bronstein, M.M. Bronstein, R. Kimmel, N. Sochen, Computers &#38; Graphics 35 (2011) 692–697.","ama":"Raviv D, Bronstein AM, Bronstein MM, Kimmel R, Sochen N. Affine-invariant geodesic geometry of deformable 3D shapes. <i>Computers &#38; Graphics</i>. 2011;35(3):692-697. doi:<a href=\"https://doi.org/10.1016/j.cag.2011.03.030\">10.1016/j.cag.2011.03.030</a>","ista":"Raviv D, Bronstein AM, Bronstein MM, Kimmel R, Sochen N. 2011. Affine-invariant geodesic geometry of deformable 3D shapes. Computers &#38; Graphics. 35(3), 692–697.","ieee":"D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, and N. Sochen, “Affine-invariant geodesic geometry of deformable 3D shapes,” <i>Computers &#38; Graphics</i>, vol. 35, no. 3. Elsevier, pp. 692–697, 2011.","apa":"Raviv, D., Bronstein, A. M., Bronstein, M. M., Kimmel, R., &#38; Sochen, N. (2011). Affine-invariant geodesic geometry of deformable 3D shapes. <i>Computers &#38; Graphics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.cag.2011.03.030\">https://doi.org/10.1016/j.cag.2011.03.030</a>"},"quality_controlled":"1","OA_place":"repository","article_processing_charge":"No"}