{"status":"public","_id":"18355","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0920-5691","1573-1405"]},"doi":"10.1007/s11263-007-0078-4","author":[{"id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein","first_name":"Alexander"},{"first_name":"Michael M.","full_name":"Bronstein, Michael M.","last_name":"Bronstein"},{"first_name":"Alfred M.","last_name":"Bruckstein","full_name":"Bruckstein, Alfred M."},{"first_name":"Ron","last_name":"Kimmel","full_name":"Kimmel, Ron"}],"extern":"1","day":"01","intvolume":"        78","publisher":"Springer Nature","date_published":"2008-06-01T00:00:00Z","oa_version":"None","citation":{"short":"A.M. Bronstein, M.M. Bronstein, A.M. Bruckstein, R. Kimmel, International Journal of Computer Vision 78 (2008) 67–88.","chicago":"Bronstein, Alex M., Michael M. Bronstein, Alfred M. Bruckstein, and Ron Kimmel. “Analysis of Two-Dimensional Non-Rigid Shapes.” <i>International Journal of Computer Vision</i>. Springer Nature, 2008. <a href=\"https://doi.org/10.1007/s11263-007-0078-4\">https://doi.org/10.1007/s11263-007-0078-4</a>.","mla":"Bronstein, Alex M., et al. “Analysis of Two-Dimensional Non-Rigid Shapes.” <i>International Journal of Computer Vision</i>, vol. 78, Springer Nature, 2008, pp. 67–88, doi:<a href=\"https://doi.org/10.1007/s11263-007-0078-4\">10.1007/s11263-007-0078-4</a>.","apa":"Bronstein, A. M., Bronstein, M. M., Bruckstein, A. M., &#38; Kimmel, R. (2008). Analysis of two-dimensional non-rigid shapes. <i>International Journal of Computer Vision</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11263-007-0078-4\">https://doi.org/10.1007/s11263-007-0078-4</a>","ieee":"A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, and R. Kimmel, “Analysis of two-dimensional non-rigid shapes,” <i>International Journal of Computer Vision</i>, vol. 78. Springer Nature, pp. 67–88, 2008.","ista":"Bronstein AM, Bronstein MM, Bruckstein AM, Kimmel R. 2008. Analysis of two-dimensional non-rigid shapes. International Journal of Computer Vision. 78, 67–88.","ama":"Bronstein AM, Bronstein MM, Bruckstein AM, Kimmel R. Analysis of two-dimensional non-rigid shapes. <i>International Journal of Computer Vision</i>. 2008;78:67-88. doi:<a href=\"https://doi.org/10.1007/s11263-007-0078-4\">10.1007/s11263-007-0078-4</a>"},"article_processing_charge":"No","OA_type":"closed access","quality_controlled":"1","year":"2008","date_created":"2024-10-15T11:20:54Z","date_updated":"2024-10-22T07:22:49Z","volume":78,"abstract":[{"lang":"eng","text":"Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper."}],"article_type":"original","title":"Analysis of two-dimensional non-rigid shapes","scopus_import":"1","publication_status":"published","page":"67-88","type":"journal_article","language":[{"iso":"eng"}],"month":"06","publication":"International Journal of Computer Vision"}