[{"quality_controlled":"1","status":"public","abstract":[{"lang":"eng","text":"Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo nonrigid deformations and only partial views are available, the problem becomes very challenging. In this chapter we describe recent techniques designed to tackle such problems. Specifically, we explain how the renown functional maps framework can be extended to tackle the partial setting. We then present a further extension to the multipart case in which one tries to establish correspondence between a collection of shapes. Finally, we focus on improving the technique efficiency, by disposing of its spatial ingredient and thus keeping the computation in the spectral domain. Extensive experimental results are provided along with the theoretical explanations, to demonstrate the effectiveness of the described methods in these challenging scenarios."}],"language":[{"iso":"eng"}],"type":"book_chapter","author":[{"last_name":"Litany","first_name":"Or","full_name":"Litany, Or"},{"first_name":"Emanuele","last_name":"Rodolà","full_name":"Rodolà, Emanuele"},{"first_name":"Alexander","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander","orcid":"0000-0001-9699-8730"},{"first_name":"Michael","last_name":"Bronstein","full_name":"Bronstein, Michael"},{"first_name":"Daniel","last_name":"Cremers","full_name":"Cremers, Daniel"}],"date_updated":"2025-01-23T13:43:17Z","scopus_import":"1","date_created":"2024-10-09T07:47:10Z","publication":"Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1","year":"2018","publication_status":"published","intvolume":"        19","date_published":"2018-11-08T00:00:00Z","extern":"1","month":"11","publisher":"Elsevier","oa_version":"None","citation":{"short":"O. Litany, E. Rodolà, A.M. Bronstein, M. Bronstein, D. Cremers, in:, R. Kimmel, X.-C. Tai (Eds.), Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1, 1st ed., Elsevier, Amsterdam, 2018, pp. 55–90.","apa":"Litany, O., Rodolà, E., Bronstein, A. M., Bronstein, M., &#38; Cremers, D. (2018). Partial Single- and Multishape Dense Correspondence Using Functional Maps. In R. Kimmel &#38; X.-C. Tai (Eds.), <i>Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1</i> (1st ed., Vol. 19, pp. 55–90). Amsterdam: Elsevier. <a href=\"https://doi.org/10.1016/bs.hna.2018.09.002\">https://doi.org/10.1016/bs.hna.2018.09.002</a>","mla":"Litany, Or, et al. “Partial Single- and Multishape Dense Correspondence Using Functional Maps.” <i>Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1</i>, edited by Ron Kimmel and Xue-Cheng Tai, 1st ed., vol. 19, Elsevier, 2018, pp. 55–90, doi:<a href=\"https://doi.org/10.1016/bs.hna.2018.09.002\">10.1016/bs.hna.2018.09.002</a>.","chicago":"Litany, Or, Emanuele Rodolà, Alex M. Bronstein, Michael Bronstein, and Daniel Cremers. “Partial Single- and Multishape Dense Correspondence Using Functional Maps.” In <i>Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1</i>, edited by Ron Kimmel and Xue-Cheng Tai, 1st ed., 19:55–90. Amsterdam: Elsevier, 2018. <a href=\"https://doi.org/10.1016/bs.hna.2018.09.002\">https://doi.org/10.1016/bs.hna.2018.09.002</a>.","ama":"Litany O, Rodolà E, Bronstein AM, Bronstein M, Cremers D. Partial Single- and Multishape Dense Correspondence Using Functional Maps. In: Kimmel R, Tai X-C, eds. <i>Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1</i>. Vol 19. 1st ed. Amsterdam: Elsevier; 2018:55-90. doi:<a href=\"https://doi.org/10.1016/bs.hna.2018.09.002\">10.1016/bs.hna.2018.09.002</a>","ieee":"O. Litany, E. Rodolà, A. M. Bronstein, M. Bronstein, and D. Cremers, “Partial Single- and Multishape Dense Correspondence Using Functional Maps,” in <i>Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1</i>, 1st ed., vol. 19, R. Kimmel and X.-C. Tai, Eds. Amsterdam: Elsevier, 2018, pp. 55–90.","ista":"Litany O, Rodolà E, Bronstein AM, Bronstein M, Cremers D. 2018.Partial Single- and Multishape Dense Correspondence Using Functional Maps. In: Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 1. Handbook of Numerical Analysis, vol. 19, 55–90."},"editor":[{"full_name":"Kimmel, Ron","last_name":"Kimmel","first_name":"Ron"},{"last_name":"Tai","first_name":"Xue-Cheng","full_name":"Tai, Xue-Cheng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","title":"Partial Single- and Multishape Dense Correspondence Using Functional Maps","place":"Amsterdam","_id":"18281","day":"08","publication_identifier":{"issn":["1570-8659"],"isbn":["9780444642059"]},"page":"55-90","fulldoi":"https://doi.org/10.1016/bs.hna.2018.09.002","edition":"1","doi":"10.1016/bs.hna.2018.09.002","alternative_title":["Handbook of Numerical Analysis"],"article_processing_charge":"No","volume":19}]