{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T05:10:40Z","timestamp":1707023440957},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2006,3,13]],"date-time":"2006-03-13T00:00:00Z","timestamp":1142208000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2006,5]]},"DOI":"10.1007\/s10851-005-3631-1","type":"journal-article","created":{"date-parts":[[2006,5,1]],"date-time":"2006-05-01T11:19:07Z","timestamp":1146482347000},"page":"327-340","source":"Crossref","is-referenced-by-count":3,"title":["Mathematical Analysis of An Extended Mumford-Shah Model for Image Segmentation"],"prefix":"10.1007","volume":"24","author":[{"given":"Trevor Chi-Yuen","family":"Tao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David James","family":"Crisp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"van der Hoek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2006,3,13]]},"reference":[{"key":"3631_CR1","doi-asserted-by":"crossref","unstructured":"L. Ambrosio, N. Fusco, and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, 2000.","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"3631_CR2","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1002\/cpa.3160430805","volume":"43","author":"L. Ambrosio","year":"1990","unstructured":"L. Ambrosio and V. Tortorelli, \u201cApproximation of functionals depending on jumps by elliptic functionals via gamma convergence,\u201d Commun. Pure Appl. Math., Vol. 43, pp. 999\u20131036, 1990.","journal-title":"Commun. Pure Appl. Math."},{"key":"3631_CR3","first-page":"105","volume":"6-B","author":"L. Ambrosio","year":"1992","unstructured":"L. Ambrosio and V. Tortorelli, \u201cOn the approximation of free discontinuity problems,\u201d Boll. Un. Mat. Ital, Vol. 6-B, pp. 105\u2013 123, 1992.","journal-title":"Boll. Un. Mat. Ital"},{"key":"3631_CR4","doi-asserted-by":"crossref","unstructured":"G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, Springer-Verlag, 2002.","DOI":"10.1007\/b97428"},{"key":"3631_CR5","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/7132.001.0001","volume-title":"Visual reconstruction","author":"A. Blake","year":"1987","unstructured":"A. Blake and A. Zisserman, Visual Reconstruction, MIT Press: Cambridge MA, 1987."},{"key":"3631_CR6","volume-title":"Bayesian inference in statistical analysis","author":"G. Box","year":"1973","unstructured":"G. Box and G. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley Pub. Co., Reading, Mass., 1973."},{"issue":"3","key":"3631_CR7","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1137\/S0036139993257132","volume":"55","author":"A. Chambolle","year":"1995","unstructured":"A. Chambolle, \u201cImage segmentation by variational methods: Mumford-Shah functional and the discrete approximations\u201d SIAM Appl. Math., Vol. 55 No. 3, pp. 827\u2013863, 1995.","journal-title":"SIAM Appl. Math"},{"issue":"4","key":"3631_CR8","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1051\/m2an:1999156","volume":"33","author":"Antonin Chambolle","year":"1999","unstructured":"Antonin Chambolle and G. Dal Maso, \u201cDiscrete approximation of the mumford-shah functional in dimension two,\u201d M2AN, Vol. 33, No. 4, pp. 651\u2013672, 1999.","journal-title":"M2AN"},{"key":"3631_CR9","unstructured":"D. Crisp and G. Newsam, \u201cA fast efficient segmentation algorithm based on region merging,\u201d In Proceedings of the IVCNZ, 2000, pp. 180\u2013185."},{"issue":"14-A","key":"3631_CR10","first-page":"213","volume":"5","author":"E. Georgi de","year":"1977","unstructured":"E. de Georgi, Gamma-convergenza e g-convergenza, Boll. Un. Mat. Ital, Vol. 5, No. 14-A, pp. 213\u2013220, 1977.","journal-title":"Boll. Un. Mat. Ital"},{"key":"3631_CR11","unstructured":"L. Evans and R. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992."},{"issue":"6","key":"3631_CR12","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"D. Geman","year":"1984","unstructured":"D. Geman and S. Geman, \u201cStochastic relaxation, Gibbs distributions and the Bayesian restoration of images\u201d IEEE Trans. PAMI, Vol. 6, No. 6, pp. 721\u2013741, 1984.","journal-title":"IEEE Trans. PAMI"},{"key":"3631_CR13","doi-asserted-by":"crossref","unstructured":"T. Kanungo, B. Dom, W. Niblack, D.Steele, and J.Cheinvald, \u201cMDL based multi-band image segmentation using a fast region merging scheme,\u201d Technical report, IBM Research Report RJ-9960 (87919), 1995.","DOI":"10.1109\/CVPR.1994.323792"},{"key":"3631_CR14","doi-asserted-by":"crossref","unstructured":"G. Koepfler, J.M. Morel, and S. Solimini, \u201cSegmentation by minimizing a functional and the merging methods, SIAM J. on Numer. Anal., Vol. 31, No. 1, 1994.","DOI":"10.1137\/0731015"},{"key":"3631_CR15","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF00054839","volume":"3","author":"Y. G. Leclerc","year":"1989","unstructured":"Y.G. Leclerc, \u201cConstructing simple stable descriptions for image partitioning,\u201d International Journal of Computer Vision, Vol. 3, pp. 73\u2013102, 1989.","journal-title":"International Journal of Computer Vision"},{"issue":"449","key":"3631_CR16","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1080\/01621459.2000.10473919","volume":"95","author":"T. Lee","year":"2000","unstructured":"T. Lee, \u201cA minimum description length based image segmentation procedure and its comparison with a cross-validation based segmentation procedure,\u201d Journal of American Stat. Assoc., Vol. 95, No. 449, pp. 259\u2013270, 2000.","journal-title":"Journal of American Stat. Assoc."},{"key":"3631_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0327-8","volume-title":"An introduction to gamma convergence","author":"G. Dal Maso","year":"1993","unstructured":"G. Dal Maso, An Introduction to Gamma Convergence, Birkh\u00e4auser, Boston, 1993."},{"key":"3631_CR18","doi-asserted-by":"crossref","unstructured":"J.M. Morel and S. Solimini, Variational Methods in Image Segmentation, chapter 5, Birkh\u00e4ser, 1995.","DOI":"10.1007\/978-1-4684-0567-5"},{"key":"3631_CR19","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"D. Mumford and J. Shah, \u201cOptimal approximations by piecewise smooth functions and associated variational problems,\u201d Commun. Pure Appl. Math., Vol. 42, pp. 577\u2013685, 1989.","journal-title":"Commun. Pure Appl. Math."},{"key":"3631_CR20","doi-asserted-by":"crossref","unstructured":"T Richardson and S Mitter, \u201cApproximation, computation and distortion in the variational formulation,\u201d Geometry-Driven Diffusion in Computer Vision, 1994.","DOI":"10.1007\/978-94-017-1699-4_8"},{"key":"3631_CR21","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/0005-1098(78)90005-5","volume":"14","author":"J. Rissanen","year":"1978","unstructured":"J. Rissanen, \u201cModeling by shortest data description,\u201d Automatica, Vol. 14, pp. 465\u2013471, 1978.","journal-title":"Automatica"},{"key":"3631_CR22","unstructured":"T. Tao and D. Crisp, \u201cA useful bound for region merging algorithms in a bayesian model,\u201d In ACCV, Adelaide, Australia, 2003, pp. 95\u2013100."},{"issue":"9","key":"3631_CR23","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1109\/34.537343","volume":"18","author":"S. Zhu","year":"1996","unstructured":"S. Zhu and A. Yuille, \u201cRegion competition: unifying snakes, region growing and bayes\/mdl for image segmentation,\u201d PAMI, Vol. 18, No. 9, pp. 884\u2013900, 1996.","journal-title":"PAMI"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-005-3631-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-005-3631-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-005-3631-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T04:52:53Z","timestamp":1707022373000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-005-3631-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3,13]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,5]]}},"alternative-id":["3631"],"URL":"https:\/\/doi.org\/10.1007\/s10851-005-3631-1","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3,13]]}}}