{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T19:16:06Z","timestamp":1696360566364},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,9,11]],"date-time":"2014-09-11T00:00:00Z","timestamp":1410393600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2015,3]]},"DOI":"10.1007\/s10851-014-0535-y","type":"journal-article","created":{"date-parts":[[2014,9,10]],"date-time":"2014-09-10T19:18:15Z","timestamp":1410376695000},"page":"451-464","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["r-Regularity"],"prefix":"10.1007","volume":"51","author":[{"given":"Pedro","family":"Duarte","sequence":"first","affiliation":[]},{"given":"Maria Joana","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,9,11]]},"reference":[{"key":"535_CR1","doi-asserted-by":"crossref","unstructured":"K\u00f6the, U., Stelldinger, P.: Shape preservation digitization of ideal and blurred binary images. In: Proceedings of the Discrete Geometry for Computer Imagery, pp. 82\u201391 (2003).","DOI":"10.1007\/978-3-540-39966-7_7"},{"issue":"2","key":"535_CR2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1023\/A:1008273227913","volume":"8","author":"LJ Latecki","year":"1998","unstructured":"Latecki, L.J., Conrad, C., Gross, A.: Preserving topology by a digitization process. J. Math. Imaging Vis. 8(2), 131\u2013159 (1998)","journal-title":"J. Math. Imaging Vis."},{"key":"535_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-93208-3","volume-title":"Algorithms for Graphics and Image Processing","author":"T Pavlidis","year":"1982","unstructured":"Pavlidis, T.: Algorithms for Graphics and Image Processing. Computer Science Press, Rockville, MD (1982)"},{"key":"535_CR4","volume-title":"Image Analysis and Mathematical Morphology","author":"J Serra","year":"1982","unstructured":"Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, Waltham (1982)"},{"key":"535_CR5","volume-title":"Image Digitization and its Influence on Shape Properties in Finite Dimensions","author":"P Stelldinger","year":"2007","unstructured":"Stelldinger, P.: Image Digitization and its Influence on Shape Properties in Finite Dimensions. IOS Press, Germany (2007)"},{"key":"535_CR6","doi-asserted-by":"crossref","unstructured":"Stelldinger, P., K\u00f6the, U.: Shape preservation during digitization: tight bounds based on the morphing distance. In: Proceedings of the Symposium Deutsche Arbeitsgemeinschaft f\u00fcr Mustererkennung, pp. 108\u2013115 (2003).","DOI":"10.1007\/978-3-540-45243-0_15"},{"issue":"1","key":"535_CR7","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1109\/TPAMI.2007.250604","volume":"29","author":"P Stelldinger","year":"2007","unstructured":"Stelldinger, P., Latecki, L.J., Siqueira, M.: Topological equivalence between a 3D Object and the reconstruction of its digital image. IEEE Trans. Pattern Anal. Mach. Intell. 29(1), 126\u2013140 (2007)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"3","key":"535_CR8","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.dam.2008.05.031","volume":"157","author":"H Meine","year":"2009","unstructured":"Meine, H., K\u00f6the, U., Stelldinger, P.: A topological sampling theorem for robust boundary reconstruction and image segmentation. Discrete Appl. Math. 157(3), 524\u2013541 (2009)","journal-title":"Discrete Appl. Math."},{"key":"535_CR9","doi-asserted-by":"crossref","unstructured":"Stelldinger, P.: Topological correct surface reconstruction using alpha shapes and relations to ball-pivoting. In: Proceedings of the International Conference on Pattern Recognition (2008).","DOI":"10.1109\/ICPR.2008.4761263"},{"issue":"8","key":"535_CR10","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1016\/j.patcog.2008.11.031","volume":"42","author":"P Stelldinger","year":"2009","unstructured":"Stelldinger, P., Tcherniavski, L.: Provably correct reconstruction of surfaces from sparse noisy samples. Pattern Recogn. 42(8), 1650\u20131659 (2009)","journal-title":"Pattern Recogn."},{"key":"535_CR11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1017\/S0143385705000301","volume":"26","author":"P Duarte","year":"2006","unstructured":"Duarte, P., Torres, M.J.: Combinatorial stability of non-deterministic systems. Erg. Theory Dyn. Syst. 26, 93\u2013128 (2006)","journal-title":"Erg. Theory Dyn. Syst."},{"issue":"1","key":"535_CR12","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/s10851-012-0397-0","volume":"48","author":"P Duarte","year":"2014","unstructured":"Duarte, P., Torres, M.J.: Smoothness of boundaries of regular sets. J. Math. Imaging Vis. 48(1), 106\u2013113 (2014)","journal-title":"J. Math. Imaging Vis."},{"key":"535_CR13","volume-title":"Calculus On Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus","author":"M Spivak","year":"1971","unstructured":"Spivak, M.: Calculus On Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. Westview Press, Boulder (1971)"},{"key":"535_CR14","volume-title":"Geometric Measure Theory","author":"H Federer","year":"1969","unstructured":"Federer, H.: Geometric Measure Theory. Springer, Berlin (1969)"},{"key":"535_CR15","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0925-7721(98)00013-3","volume":"10","author":"D Attali","year":"1998","unstructured":"Attali, D.: r-Regular shape reconstruction from unorganized points. Comput. Geom.: Theory Appl. 10, 239\u2013247 (1998)","journal-title":"Comput. Geom.: Theory Appl."},{"key":"535_CR16","unstructured":"Bernardini, F., Bajaj, C.L.: Sampling and reconstructing manifolds using $$\\alpha $$ \u03b1 -shapes. In: Proceedings of the 9th Canadian Conference on Computational Geometry, pp. 193\u2013198 (1997)."},{"key":"535_CR17","doi-asserted-by":"crossref","unstructured":"Burago, D., Burago, Y., Ivanov, S.: A Course in Metric Geometry. American Mathematical Society, Providence (2001).","DOI":"10.1090\/gsm\/033"},{"key":"535_CR18","unstructured":"Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkh\u00e4user, Basel (1990)."},{"key":"535_CR19","volume-title":"Real and Complex Analysis","author":"W Rudin","year":"1986","unstructured":"Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1986)"},{"key":"535_CR20","unstructured":"Hinton, D.: Sturm\u2019s 1836 oscillation results evolution of the theory. Sturm-Liouville theory, pp. 1\u201327. Birkh\u00e4user, Basel (2005)."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-014-0535-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-014-0535-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-014-0535-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T02:26:24Z","timestamp":1559269584000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-014-0535-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,11]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["535"],"URL":"https:\/\/doi.org\/10.1007\/s10851-014-0535-y","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,11]]}}}