{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T15:48:54Z","timestamp":1742917734661,"version":"3.40.3"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030926588"},{"type":"electronic","value":"9783030926595"}],"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.springer.com\/tdm"},{"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.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-92659-5_32","type":"book-chapter","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T07:09:18Z","timestamp":1642057758000},"page":"498-512","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Assignment Flows and\u00a0Nonlocal PDEs on\u00a0Graphs"],"prefix":"10.1007","author":[{"given":"Dmitrij","family":"Sitenko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bastian","family":"Boll","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"32_CR1","unstructured":"Amari, S.I., Nagaoka, H.: Methods of Information Geometry. American Mathematical Society and Oxford University Press, Oxford (2000)"},{"issue":"8","key":"32_CR2","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1002\/cpa.3160430805","volume":"43","author":"L Ambrosio","year":"1990","unstructured":"Ambrosio, L., Tortorelli, V.M.: Approximation of functional depending on jumps by elliptic functional via $$\\varGamma $$-convergence. Commun. Pure Appl. Math. 43(8), 999\u20131036 (1990)","journal-title":"Commun. Pure Appl. Math."},{"issue":"2","key":"32_CR3","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s10851-016-0702-4","volume":"58","author":"F \u00c5str\u00f6m","year":"2017","unstructured":"\u00c5str\u00f6m, F., Petra, S., Schmitzer, B., Schn\u00f6rr, C.: Image labeling by assignment. J. Math. Imaging Vis. 58(2), 211\u2013238 (2017)","journal-title":"J. Math. Imaging Vis."},{"key":"32_CR4","doi-asserted-by":"crossref","unstructured":"Ay, N., Jost, J., L\u00ea, H.V., Schwachh\u00f6fer, L.: Information Geometry. Springer, Heidelberg (2017)","DOI":"10.1007\/978-3-319-56478-4"},{"issue":"2","key":"32_CR5","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1137\/16M1070426","volume":"58","author":"A Bertozzi","year":"2016","unstructured":"Bertozzi, A., Flenner, A.: Diffuse interface models on graphs for classification of high dimensional data. SIAM Rev. 58(2), 293\u2013328 (2016)","journal-title":"SIAM Rev."},{"key":"32_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00211-006-0029-y","volume":"105","author":"A Buades","year":"2006","unstructured":"Buades, A., Coll, B., Morel, J.M.: Neighborhood filter and PDEs. Numer. Math. 105, 1\u201334 (2006)","journal-title":"Numer. Math."},{"issue":"1","key":"32_CR7","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1137\/090773908","volume":"52","author":"A Buades","year":"2010","unstructured":"Buades, A., Coll, B., Morel, J.M.: Image denoising methods. A new nonlocal principle. SIAM Rev. 52(1), 113\u2013147 (2010)","journal-title":"SIAM Rev."},{"key":"32_CR8","unstructured":"Chen, R.T.Q., Rubanova, Y., Bettencourt, J., Duvenaud, D.: Neural ordinary differential equations. In: Proceedings of the NeurIPS (2018)"},{"key":"32_CR9","unstructured":"Chung, F.: Spectral Graph Theory. American Mathematical Society, Ann Arbor (1997)"},{"issue":"2","key":"32_CR10","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1006\/jcta.1996.0080","volume":"5","author":"F Chung","year":"1996","unstructured":"Chung, F., Langlands, R.P.: A combinatorial Laplacian with vertex weights. J. Comb. Theory Seri. A 5(2), 316\u2013327 (1996)","journal-title":"J. Comb. Theory Seri. A"},{"key":"32_CR11","doi-asserted-by":"crossref","unstructured":"Du, Q.: Nonlocal Modeling, Analysis, and Computation. SIAM, Philadelphia (2019)","DOI":"10.1137\/1.9781611975628"},{"issue":"3","key":"32_CR12","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1142\/S0218202512500546","volume":"23","author":"Q Du","year":"2013","unstructured":"Du, Q., Gunzburger, M., Lehoucq, R.B., Zhou, K.: A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Math. Models Meth. Appl. Sci. 23(3), 493\u2013540 (2013)","journal-title":"Math. Models Meth. Appl. Sci."},{"issue":"4","key":"32_CR13","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1137\/110833294","volume":"54","author":"Q Du","year":"2012","unstructured":"Du, Q., Gunzburger, M., Lehoucq, R.B., Zhou, K.: Analysis and approximation of nonlocal diffusion problems with volume constraints. SIAM Rev. 54(4), 667\u2013696 (2012)","journal-title":"SIAM Rev."},{"issue":"7","key":"32_CR14","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1109\/TIP.2008.924284","volume":"17","author":"A Elmoataz","year":"2008","unstructured":"Elmoataz, A., Lezoray, O., Bougleux, S.: Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing. IEEE Trans. Image Proc. 17(7), 1047\u20131059 (2008)","journal-title":"IEEE Trans. Image Proc."},{"issue":"4","key":"32_CR15","doi-asserted-by":"publisher","first-page":"2412","DOI":"10.1137\/15M1022793","volume":"8","author":"A Elmoataz","year":"2015","unstructured":"Elmoataz, A., Toutain, M., Tenbrinck, D.: On the $$p$$-Laplacian and $$\\infty $$-Laplacian on graphs with applications in image and data processing. SIAM J. Imag. Sci. 8(4), 2412\u20132451 (2015)","journal-title":"SIAM J. Imag. Sci."},{"issue":"3","key":"32_CR16","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1137\/070698592","volume":"7","author":"G Gilboa","year":"2009","unstructured":"Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005\u20131028 (2009)","journal-title":"Multiscale Model. Simul."},{"issue":"1","key":"32_CR17","doi-asserted-by":"publisher","first-page":"014004","DOI":"10.1088\/1361-6420\/aa9a90","volume":"34","author":"E Haber","year":"2017","unstructured":"Haber, E., Ruthotto, L.: Stable architectures for deep neural networks. Inverse Prob. 34(1), 014004 (2017)","journal-title":"Inverse Prob."},{"key":"32_CR18","doi-asserted-by":"crossref","unstructured":"Minaee, S., Boykov, Y.Y., Porikli, F., Plaza, A.J., Kehtarnavaz, N., Terzopoulos, D.: Image segmentation using deep learning: a survey. IEEE Trans. Pattern Anal. Mach. Intell. (2021). https:\/\/ieeexplore.ieee.org\/document\/9356353","DOI":"10.1109\/TPAMI.2021.3059968"},{"issue":"3","key":"32_CR19","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1017\/S0956792520000273","volume":"32","author":"F Savarino","year":"2021","unstructured":"Savarino, F., Schn\u00f6rr, C.: Continuous-domain assignment flows. Eur. J. Appl. Math. 32(3), 570\u2013597 (2021)","journal-title":"Eur. J. Appl. Math."},{"key":"32_CR20","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-030-31351-7_8","volume-title":"Handbook of Variational Methods for Nonlinear Geometric Data","author":"C Schn\u00f6rr","year":"2020","unstructured":"Schn\u00f6rr, C.: Assignment flows. In: Grohs, P., Holler, M., Weinmann, A. (eds.) Handbook of Variational Methods for Nonlinear Geometric Data, pp. 235\u2013260. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-31351-7_8"},{"key":"32_CR21","unstructured":"Weickert, J.: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998)"},{"key":"32_CR22","doi-asserted-by":"crossref","unstructured":"Zeilmann, A., Savarino, F., Petra, S., Schn\u00f6rr, C.: Geometric numerical integration of the assignment flow. Inverse Probl. 36(3), 034004 (2020). (33pp)","DOI":"10.1088\/1361-6420\/ab2772"},{"key":"32_CR23","doi-asserted-by":"crossref","unstructured":"Zern, A., Zeilmann, A., Schn\u00f6rr, C.: Assignment Flows for Data Labeling on Graphs: Convergence and Stability. CoRR abs\/2002.11571 (2020)","DOI":"10.1007\/s41884-021-00060-8"}],"container-title":["Lecture Notes in Computer Science","Pattern Recognition"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-92659-5_32","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,5]],"date-time":"2022-05-05T14:51:33Z","timestamp":1651762293000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-92659-5_32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030926588","9783030926595"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-92659-5_32","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":"13 January 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DAGM GCPR","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"DAGM German Conference on Pattern Recognition","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bonn","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","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":"28 September 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 October 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"43","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dagm2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.dagm-gcpr.de\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"CMT","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"116","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":"46","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":"40% - 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":"2.95","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":"4.3","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":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held virtually due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}