{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T14:30:42Z","timestamp":1743085842494,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642382932"},{"type":"electronic","value":"9783642382949"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-38294-9_4","type":"book-chapter","created":{"date-parts":[[2013,5,13]],"date-time":"2013-05-13T02:52:56Z","timestamp":1368413576000},"page":"37-48","source":"Crossref","is-referenced-by-count":19,"title":["Discrete Set-Valued Continuity and Interpolation"],"prefix":"10.1007","author":[{"given":"Laurent","family":"Najman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thierry","family":"G\u00e9raud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"3","key":"4_CR1","first-page":"501","volume":"2","author":"P. Alexandroff","year":"1937","unstructured":"Alexandroff, P.: Diskrete R\u00e4ume. Math. Sbornik\u00a02(3), 501\u2013518 (1937)","journal-title":"Math. Sbornik"},{"unstructured":"Alexandroff, P.: Combinatorial topology. Dover Publications (1947)","key":"4_CR2"},{"unstructured":"Arenas, F.: Alexandroff spaces. Acta Math. Univ. Comen.\u00a0LXVIII(1), 17\u201325 (1999)","key":"4_CR3"},{"doi-asserted-by":"crossref","unstructured":"Aubin, J., Frankowska, H.: Set-valued analysis. Birkhauser (2008)","key":"4_CR4","DOI":"10.1007\/978-0-8176-4848-0"},{"doi-asserted-by":"crossref","unstructured":"Bertrand, G., Couprie, M.: A model for digital topology. Discrete Geometry for Computer Imagery, 229\u2013241 (1999)","key":"4_CR5","DOI":"10.1007\/3-540-49126-0_18"},{"issue":"8","key":"4_CR6","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1016\/0167-8655(94)90012-4","volume":"15","author":"L. Boxer","year":"1994","unstructured":"Boxer, L.: Digitally continuous functions. PRL\u00a015(8), 833\u2013839 (1994)","journal-title":"PRL"},{"doi-asserted-by":"crossref","unstructured":"Caselles, V., Monasse, P.: Geometric description of topographic maps. Lecture Notes in Mathematics, vol.\u00a01984. Springer (2010)","key":"4_CR7","DOI":"10.1007\/978-3-642-04611-7"},{"issue":"1","key":"4_CR8","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1007\/s10851-011-0277-z","volume":"42","author":"C. Escribano","year":"2012","unstructured":"Escribano, C., Giraldo, A., Sastre, M.A.: Digitally continuous multivalued functions, morphological operations and thinning algorithms. JMIV\u00a042(1), 76\u201391 (2012)","journal-title":"JMIV"},{"key":"4_CR9","doi-asserted-by":"publisher","first-page":"1553","DOI":"10.1007\/BF00670697","volume":"33","author":"A. Evako","year":"1996","unstructured":"Evako, A.: Dimension on discrete spaces. International Journal of Theoretical Physics\u00a033, 1553\u20131568 (1996)","journal-title":"International Journal of Theoretical Physics"},{"key":"4_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/978-3-642-38294-9_9","volume-title":"ISMM 2013","author":"T. G\u00e9raud","year":"2013","unstructured":"G\u00e9raud, T., Carlinet, E., Crozet, S., Najman, L.: A quasi-linear algorithm to compute the tree of shapes of nD images. In: Luengo Hendriks, C.L., Borgefors, G., Strand, R. (eds.) ISMM 2013. LNCS, vol.\u00a07883, pp. 98\u2013110. Springer, Heidelberg (2013)"},{"key":"4_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/978-3-642-19867-0_13","volume-title":"Discrete Geometry for Computer Imagery","author":"R. Gonzalez-Diaz","year":"2011","unstructured":"Gonzalez-Diaz, R., Jimenez, M.-J., Medrano, B.: Well-composed cell complexes. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds.) DGCI 2011. LNCS, vol.\u00a06607, pp. 153\u2013162. Springer, Heidelberg (2011)"},{"key":"4_CR12","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-662-03039-4_4","volume":"126","author":"W. Kovalevsky","year":"1994","unstructured":"Kovalevsky, W.: A new concept for digital geometry. Shape in Pictures, NATO ASI Series F\u00a0126, 37\u201351 (1994)","journal-title":"Shape in Pictures, NATO ASI Series F"},{"issue":"1","key":"4_CR13","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1006\/cviu.1995.1006","volume":"61","author":"L. Latecki","year":"1995","unstructured":"Latecki, L., Eckhardt, U., Rosenfeld, A.: Well-composed sets. Computer Vision and Image Understanding\u00a061(1), 70\u201383 (1995)","journal-title":"Computer Vision and Image Understanding"},{"issue":"3","key":"4_CR14","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1006\/gmip.1997.0422","volume":"59","author":"L. Latecki","year":"1997","unstructured":"Latecki, L.: 3d well-composed pictures. CVGIP: Graphical Model and Image Processing\u00a059(3), 164\u2013172 (1997)","journal-title":"CVGIP: Graphical Model and Image Processing"},{"issue":"5","key":"4_CR15","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/j.patrec.2003.12.005","volume":"25","author":"J. Marchadier","year":"2004","unstructured":"Marchadier, J., Arqu\u00e8s, D., Michelin, S.: Thinning grayscale well-composed images. PRL\u00a025(5), 581\u2013590 (2004)","journal-title":"PRL"},{"issue":"5","key":"4_CR16","first-page":"860","volume":"9","author":"P. Monasse","year":"2000","unstructured":"Monasse, P., Guichard, F.: Fast computation of a contrast-invariant image representation. TIP\u00a09(5), 860\u2013872 (2000)","journal-title":"TIP"},{"key":"4_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/978-3-540-30503-3_20","volume-title":"Combinatorial Image Analysis","author":"A. Nakamura","year":"2004","unstructured":"Nakamura, A.: Magnification in digital topology. In: Klette, R., \u017duni\u0107, J. (eds.) IWCIA 2004. LNCS, vol.\u00a03322, pp. 260\u2013275. Springer, Heidelberg (2004)"},{"unstructured":"Ronse, C.: Regular open or closed sets. Tech. Rep. Working Document WD59, Philips Research Lab., Brussels (1990)","key":"4_CR18"},{"issue":"3","key":"4_CR19","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/0167-8655(86)90017-6","volume":"4","author":"A. Rosenfeld","year":"1986","unstructured":"Rosenfeld, A.: \u201cContinuous\u201d functions on digital pictures. PRL\u00a04(3), 177\u2013184 (1986)","journal-title":"PRL"},{"issue":"3","key":"4_CR20","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s10851-007-0054-1","volume":"30","author":"M. Siqueira","year":"2008","unstructured":"Siqueira, M., Latecki, L.J., Tustison, N., Gallier, J., Gee, J.: Topological repairing of 3D digital images. JMIV\u00a030(3), 249\u2013274 (2008)","journal-title":"JMIV"},{"issue":"1","key":"4_CR21","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1109\/TPAMI.2007.250604","volume":"29","author":"P. Stelldinger","year":"2007","unstructured":"Stelldinger, P., Latecki, L., Siqueira, M.: Topological equivalence between a 3d object and the reconstruction of its digital image. PAMI\u00a029(1), 126\u2013140 (2007)","journal-title":"PAMI"},{"key":"4_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/3-540-45576-0_5","volume-title":"Digital and Image Geometry","author":"R. Tsaur","year":"2002","unstructured":"Tsaur, R., Smyth, M.B.: \u201cContinuous\u201d multifunctions in discrete spaces with applications to fixed point theory. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol.\u00a02243, pp. 75\u201388. Springer, Heidelberg (2002)"},{"issue":"3","key":"4_CR23","first-page":"330","volume":"68","author":"Y. Wang","year":"1997","unstructured":"Wang, Y., Bhattacharya, P.: Digital connectivity and extended well-composed sets for gray images. CVIU\u00a068(3), 330\u2013345 (1997)","journal-title":"CVIU"}],"container-title":["Lecture Notes in Computer Science","Mathematical Morphology and Its Applications to Signal and Image Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-38294-9_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T17:45:16Z","timestamp":1674495916000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-38294-9_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642382932","9783642382949"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-38294-9_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}