{"scopus_import":"1","month":"06","year":"2011","article_processing_charge":"No","publication_identifier":{"issn":["0097-8493"]},"language":[{"iso":"eng"}],"date_created":"2024-10-15T11:20:54Z","page":"692-697","doi":"10.1016/j.cag.2011.03.030","oa":1,"oa_version":"Preprint","OA_place":"repository","author":[{"first_name":"Dan","last_name":"Raviv","full_name":"Raviv, Dan"},{"full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","first_name":"Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein"},{"last_name":"Bronstein","first_name":"Michael M.","full_name":"Bronstein, Michael M."},{"last_name":"Kimmel","first_name":"Ron","full_name":"Kimmel, Ron"},{"first_name":"Nir","last_name":"Sochen","full_name":"Sochen, Nir"}],"_id":"18363","type":"journal_article","intvolume":"        35","extern":"1","date_published":"2011-06-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1012.5936"}],"day":"01","status":"public","OA_type":"green","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","external_id":{"arxiv":["1012.5936"]},"abstract":[{"lang":"eng","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."}],"volume":35,"citation":{"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.","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>.","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>.","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>","short":"D. Raviv, A.M. Bronstein, M.M. Bronstein, R. Kimmel, N. Sochen, Computers &#38; Graphics 35 (2011) 692–697.","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.","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>"},"arxiv":1,"publisher":"Elsevier","publication":"Computers & Graphics","article_type":"letter_note","issue":"3","date_updated":"2024-11-12T08:37:24Z","quality_controlled":"1","title":"Affine-invariant geodesic geometry of deformable 3D shapes"}