{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T04:15:23Z","timestamp":1747282523591,"version":"3.40.5"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030766566"},{"type":"electronic","value":"9783030766573"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-76657-3_13","type":"book-chapter","created":{"date-parts":[[2021,5,15]],"date-time":"2021-05-15T20:02:23Z","timestamp":1621108943000},"page":"189-201","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Homotopic Digital Rigid Motion: An Optimization Approach on Cellular Complexes"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0320-4581","authenticated-orcid":false,"given":"Nicolas","family":"Passat","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7423-5932","authenticated-orcid":false,"given":"Phuc","family":"Ngo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9648-326X","authenticated-orcid":false,"given":"Yukiko","family":"Kenmochi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,16]]},"reference":[{"key":"13_CR1","doi-asserted-by":"crossref","unstructured":"Andres, \u00c9.: The quasi-shear rotation. In: DGCI, pp. 307\u2013314 (1996)","DOI":"10.1007\/3-540-62005-2_26"},{"key":"13_CR2","doi-asserted-by":"crossref","unstructured":"Andres, \u00c9., Dutt, M., Biswas, A., Largeteau-Skapin, G., Zrour, R.: Digital two-dimensional bijective reflection and associated rotation. In: DGCI, pp. 3\u201314 (2019)","DOI":"10.1007\/978-3-030-14085-4_1"},{"key":"13_CR3","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1080\/00029890.1988.11972043","volume":"95","author":"WS Anglin","year":"1988","unstructured":"Anglin, W.S.: Using Pythagorean triangles to approximate angles. Am. Math. Monthly 95, 540\u2013541 (1988)","journal-title":"Am. Math. Monthly"},{"key":"13_CR4","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1007\/s10851-018-0846-5","volume":"61","author":"\u00c9 Baudrier","year":"2019","unstructured":"Baudrier, \u00c9., Mazo, L.: Combinatorics of the Gauss digitization under translation in 2D. J. Math. Imaging Vision 61, 224\u2013236 (2019)","journal-title":"J. Math. Imaging Vision"},{"key":"13_CR5","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1016\/j.tcs.2007.03.032","volume":"380","author":"V Berth\u00e9","year":"2007","unstructured":"Berth\u00e9, V., Nouvel, B.: Discrete rotations and symbolic dynamics. Theoret. Comput. Sci. 380, 276\u2013285 (2007)","journal-title":"Theoret. Comput. Sci."},{"key":"13_CR6","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.gmod.2004.12.001","volume":"67","author":"I Bloch","year":"2005","unstructured":"Bloch, I., Pescatore, J., Garnero, L.: A new characterization of simple elements in a tetrahedral mesh. Graphical Models 67, 260\u2013284 (2005)","journal-title":"Graphical Models"},{"key":"13_CR7","doi-asserted-by":"crossref","unstructured":"Blot, V., Coeurjolly, D.: Quasi-affine transformation in higher dimension. In: DGCI, pp. 493\u2013504 (2009)","DOI":"10.1007\/978-3-642-04397-0_42"},{"key":"13_CR8","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1109\/TPAMI.2008.117","volume":"31","author":"M Couprie","year":"2009","unstructured":"Couprie, M., Bertrand, G.: New characterizations of simple points in 2D, 3D, and 4D discrete spaces. IEEE Trans. Pattern Anal. Mach. Intell. 31, 637\u2013648 (2009)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"13_CR9","unstructured":"Jacob, M.A., Andres, \u00c9.: On discrete rotations. In: DGCI, pp. 161\u2013174 (1995)"},{"key":"13_CR10","doi-asserted-by":"crossref","unstructured":"Jacob-Da Col, M., Mazo, L.: nD quasi-affine transformations. In: DGCI, pp. 337\u2013348 (2016)","DOI":"10.1007\/978-3-319-32360-2_26"},{"key":"13_CR11","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0734-189X(89)90165-5","volume":"46","author":"VA Kovalevsky","year":"1989","unstructured":"Kovalevsky, V.A.: Finite topology as applied to image analysis. Comput Vision Graphics Image Process. 46, 141\u2013161 (1989)","journal-title":"Comput Vision Graphics Image Process."},{"key":"13_CR12","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s10440-010-9591-5","volume":"113","author":"L Mazo","year":"2011","unstructured":"Mazo, L., Passat, N., Couprie, M., Ronse, C.: Paths, homotopy and reduction in digital images. Acta Applicandae Mathematicae 113, 167\u2013193 (2011)","journal-title":"Acta Applicandae Mathematicae"},{"key":"13_CR13","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1007\/s10851-018-0853-6","volume":"61","author":"L Mazo","year":"2019","unstructured":"Mazo, L.: Multi-scale arithmetization of linear transformations. J. Math. Imag. Vision 61, 432\u2013442 (2019)","journal-title":"J. Math. Imag. Vision"},{"key":"13_CR14","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.jcss.2017.08.001","volume":"95","author":"L Mazo","year":"2018","unstructured":"Mazo, L., Baudrier, \u00c9.: Object digitization up to a translation. J. Comput. Syst. Sci. 95, 193\u2013203 (2018)","journal-title":"J. Comput. Syst. Sci."},{"key":"13_CR15","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s10851-011-0308-9","volume":"44","author":"L Mazo","year":"2012","unstructured":"Mazo, L., Passat, N., Couprie, M., Ronse, C.: Digital imaging: a unified topological framework. J. Math. Imaging Vision 44, 19\u201337 (2012)","journal-title":"J. Math. Imaging Vision"},{"key":"13_CR16","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1007\/s10851-013-0474-z","volume":"49","author":"P Ngo","year":"2014","unstructured":"Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Topology-preserving conditions for 2D digital images under rigid transformations. J. Math. Imaging Vision 49, 418\u2013433 (2014)","journal-title":"J. Math. Imaging Vision"},{"key":"13_CR17","doi-asserted-by":"crossref","unstructured":"Ngo, P., Passat, N., Kenmochi, Y., Debled-Rennesson, I.: Convexity invariance of voxel objects under rigid motions. In: ICPR, pp. 1157\u20131162 (2018)","DOI":"10.1109\/ICPR.2018.8545023"},{"key":"13_CR18","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1109\/TIP.2013.2295751","volume":"23","author":"P Ngo","year":"2014","unstructured":"Ngo, P., Passat, N., Kenmochi, Y., Talbot, H.: Topology-preserving rigid transformation of 2D digital images. IEEE Trans. Image Process. 23, 885\u2013897 (2014)","journal-title":"IEEE Trans. Image Process."},{"key":"13_CR19","doi-asserted-by":"crossref","unstructured":"Nouvel, B., R\u00e9mila, E.: Characterization of bijective discretized rotations. In: IWCIA, pp. 248\u2013259 (2004)","DOI":"10.1007\/978-3-540-30503-3_19"},{"key":"13_CR20","doi-asserted-by":"crossref","unstructured":"Nouvel, B., R\u00e9mila, E.: Incremental and transitive discrete rotations. In: IWCIA, pp. 199\u2013213 (2006)","DOI":"10.1007\/11774938_16"},{"key":"13_CR21","doi-asserted-by":"crossref","unstructured":"Passat, N., Kenmochi, Y., Ngo, P., Pluta, K.: Rigid motions in the cubic grid: a discussion on topological issues. In: DGCI, pp. 127\u2013140 (2019)","DOI":"10.1007\/978-3-030-14085-4_11"},{"key":"13_CR22","doi-asserted-by":"crossref","unstructured":"Pluta, K., Moroz, G., Kenmochi, Y., Romon, P.: Quadric arrangement in classifying rigid motions of a 3D digital image. In: CASC, pp. 426\u2013443 (2016)","DOI":"10.1007\/978-3-319-45641-6_27"},{"key":"13_CR23","doi-asserted-by":"crossref","unstructured":"Pluta, K., Romon, P., Kenmochi, Y., Passat, N.: Bijectivity certification of 3D digitized rotations. In: CTIC, pp. 30\u201341 (2016)","DOI":"10.1007\/978-3-319-39441-1_4"},{"key":"13_CR24","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/s10851-017-0706-8","volume":"59","author":"K Pluta","year":"2017","unstructured":"Pluta, K., Romon, P., Kenmochi, Y., Passat, N.: Bijective digitized rigid motions on subsets of the plane. J. Math. Imaging Vision 59, 84\u2013105 (2017)","journal-title":"J. Math. Imaging Vision"},{"key":"13_CR25","unstructured":"Roussillon, T., Coeurjolly, D.: Characterization of bijective discretized rotations by Gaussian integers. Technical report (2016). https:\/\/hal.archives-ouvertes.fr\/hal-01259826"},{"key":"13_CR26","doi-asserted-by":"publisher","first-page":"1378","DOI":"10.1016\/j.tcs.2010.10.031","volume":"412","author":"Y Thibault","year":"2011","unstructured":"Thibault, Y., Sugimoto, A., Kenmochi, Y.: 3D discrete rotations using hinge angles. Theoret. Comput. Sci. 412, 1378\u20131391 (2011)","journal-title":"Theoret. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Discrete Geometry and Mathematical Morphology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-76657-3_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T22:02:38Z","timestamp":1747260158000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-76657-3_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030766566","9783030766573"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-76657-3_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"16 May 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DGMM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Discrete Geometry and Mathematical Morphology","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Uppsala","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Sweden","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 May 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 May 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dgmm2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.dgmm2021.se\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"59","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"36","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"61% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1,3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}