{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T07:56:29Z","timestamp":1792050989292,"version":"4.4.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2002,12,1]],"date-time":"2002-12-01T00:00:00Z","timestamp":1038700800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,12,1]],"date-time":"2002-12-01T00:00:00Z","timestamp":1038700800000},"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":["International Journal of Computer Vision"],"published-print":{"date-parts":[[2002,12]]},"DOI":"10.1023\/a:1020826424915","type":"journal-article","created":{"date-parts":[[2003,3,18]],"date-time":"2003-03-18T15:57:25Z","timestamp":1048003045000},"page":"295-313","source":"Crossref","is-referenced-by-count":245,"title":["Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional"],"prefix":"10.1007","volume":"50","author":[{"given":"Daniel","family":"Cremers","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Florian","family":"Tischh\u00e4user","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joachim","family":"Weickert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"issue":"4","key":"5099472_CR1","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1137\/0902035","volume":"2","author":"R.E. Alcouffe","year":"1981","unstructured":"Alcouffe, R.E., Brandt, A., Dendy, Jr.,J.E., and Painter, J.W. 1981. The multi-grid method for the diffusion equation with strongly discontinuous coefficients. SIAM J.Sci.Stat.Comp., 2(4):430\u2013454.","journal-title":"SIAM J. Sci. Stat. Comp."},{"key":"5099472_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-1555-7","volume-title":"Active Contours","author":"A. Blake","year":"1998","unstructured":"Blake, A. and Isard, M. 1998. Active Contours, Springer: London."},{"key":"5099472_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719505","volume-title":"A Multigrid Tutorial","author":"W.L. Briggs","year":"2000","unstructured":"Briggs, W.L., Henson, V.E., and McCormick, S.F. 2000. A Multigrid Tutorial, 2nd edn. SIAM: Philadelphia.","edition":"2nd edn."},{"key":"5099472_CR4","doi-asserted-by":"crossref","unstructured":"Caselles, V., Kimmel, R., and Sapiro, G. 1995. Geodesic active contours. In Proc.IEEE Internat.Conf.on Comp.Vis., Boston, USA, pp. 694\u2013699.","DOI":"10.1109\/ICCV.1995.466871"},{"key":"5099472_CR5","doi-asserted-by":"crossref","unstructured":"Chan, T. and Vese, L. 2001. A level set algorithm for minimizing the Mumford-Shah functional in image processing. In IEEE Workshop on Variational and Level Set Methods, Vancouver, CA, pp. 161\u2013168.","DOI":"10.1109\/VLSM.2001.938895"},{"key":"5099472_CR6","unstructured":"Chen, Y., Thiruvenkadam, S., Tagare, H., Huang, F., Wilson, D., and Geiser, E. 2001. On the incorporation of shape priors into geometric active contours. In IEEE Workshop on Variational and Level Set Methods, Vancouver, CA, pp. 145\u2013152."},{"issue":"1","key":"5099472_CR7","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1006\/cviu.1995.1004","volume":"61","author":"T.F. Cootes","year":"1995","unstructured":"Cootes, T.F., Taylor, C.J., Cooper, D.M., and Graham, J. 1995. Active shape models\u2014their training and application. Comp.Vision Image Underst., 61(1):38\u201359.","journal-title":"Comp. Vision Image Underst."},{"key":"5099472_CR8","series-title":"LNCS","first-page":"93","volume-title":"Proc.of the Europ.Conf.on Comp.Vis., Copenhagen","author":"D. Cremers","year":"2002","unstructured":"Cremers, D., Kohlberger, T., and Schn\u00f6rr, C. 2002. Nonlinear shape statistics in Mumford-Shah based segmentation. In Proc.of the Europ.Conf.on Comp.Vis., Copenhagen, A. Heyden et al. (Eds.), vol. 2351 of LNCS. Springer: Berlin, pp. 93\u2013108."},{"key":"5099472_CR9","volume-title":"Pattern Recognition","author":"D. Cremers","year":"2002","unstructured":"Cremers, D. and Schn\u00e4rr, C. 2002. Motion competition: Variational integration of motion segmentation and shape regularization. In Pattern Recognition, L. van Gool (Ed.), Z\u00fcrich, LNCS, Springer: Berlin."},{"key":"5099472_CR10","doi-asserted-by":"crossref","unstructured":"Cremers, D., Schn\u00f6rr, C., and Weickert, J. 2001. Diffusion snakes: Combining statistical shape knowledge and image information in a variational framework. In IEEE First Workshop on Variational and Level Set Methods, Vancouver, pp. 137\u2013144.","DOI":"10.1109\/VLSM.2001.938892"},{"key":"5099472_CR11","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/10722492_11","volume-title":"Alge-braic Frames for the Perception-Action Cycle","author":"D. Cremers","year":"2000","unstructured":"Cremers, D., Schn\u00f6rr, C., Weickert, J., and Schellewald, C. 2000. Diffusion snakes using statistical shape knowledge. In Alge-braic Frames for the Perception-Action Cycle, G. Sommer and Y.Y. Zeevi (Eds.), vol. 1888 of LNCS, pp. 164\u2013174. Springer: Berlin."},{"key":"5099472_CR12","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/0021-9991(82)90057-2","volume":"48","author":"J.E. Dendy","year":"1982","unstructured":"Dendy, J.E. 1982. Black box multigrid. J.Comp.Phys., 48:366\u2013386.","journal-title":"J. Comp. Phys."},{"key":"5099472_CR13","volume-title":"Statistical Shape Analysis","author":"I.L. Dryden","year":"1998","unstructured":"Dryden, I.L. and Mardia, K.V. 1998. Statistical Shape Analysis. Wiley: Chichester."},{"key":"5099472_CR14","volume-title":"Curves and Surfaces for Computer\u2013Aided Geometric Design","author":"G. Farin","year":"1997","unstructured":"Farin, G. 1997. Curves and Surfaces for Computer\u2013Aided Geometric Design. Academic Press: San Diego, CA."},{"issue":"2","key":"5099472_CR15","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1111\/j.2517-6161.1991.tb01825.x","volume":"53","author":"C. Goodall","year":"1991","unstructured":"Goodall, C. 1991. Procrustes methods in the statistical analysis of shape. J.Roy.Statist.Soc., Ser.B., 53(2):285\u2013339.","journal-title":"J. Roy. Statist. Soc., Ser. B."},{"key":"5099472_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3046-5","volume-title":"Hands: A Pattern Theoretic Study of Biological Shapes","author":"U. Grenander","year":"1991","unstructured":"Grenander, U., Chow, Y., and Keenan, D.M. 1991. Hands: A Pattern Theoretic Study of Biological Shapes. Springer: New York."},{"issue":"4","key":"5099472_CR17","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF00133570","volume":"1","author":"M. Kass","year":"1988","unstructured":"Kass, M., Witkin, A., and Terzopoulos, D. 1988. Snakes: Active contour models. Int.J.of Comp.Vis., 1(4):321\u2013331.","journal-title":"Int. J. of Comp. Vis."},{"key":"5099472_CR18","volume-title":"Mod\u00e8les statistiques pour la segmentation et le suivi de structures d\u00e9formables bidimensionnelles dans une s\u00e9quence d'images","author":"C. Kervrann","year":"1995","unstructured":"Kervrann, C. 1995. Mod\u00e8les statistiques pour la segmentation et le suivi de structures d\u00e9formables bidimensionnelles dans une s\u00e9quence d'images. Ph.D. Thesis, Universit\u00e9 de Rennes I, France."},{"key":"5099472_CR19","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1109\/83.753745","volume":"8","author":"C. Kervrann","year":"1999","unstructured":"Kervrann, C. and Heitz, F. 1999. Statistical deformable model-based segmentation of image motion. IEEE Trans.on Image Processing, 8:583\u2013588.","journal-title":"IEEE Trans. on Image Processing"},{"key":"5099472_CR20","doi-asserted-by":"crossref","unstructured":"Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A.J. 1995. Gradient flows and geometric active contour models. In Proc.IEEE Internat.Conf.on Comp.Vis., Boston, USA, pp. 810\u2013815.","DOI":"10.1109\/ICCV.1995.466855"},{"key":"5099472_CR21","first-page":"316","volume":"1","author":"M.E. Leventon","year":"2000","unstructured":"Leventon, M.E., Grimson, W.E.L., and Faugeras, O. 2000. Statistical shape influence in geodesic active contours. In Proc.Conf.Computer Vis.and Pattern Recog., Hilton Head Island, SC, vol. 1, pp. 316\u2013323. June 13\u201315.","journal-title":"Proc. Conf. Computer Vis. and Pattern Recog., Hilton Head Island, SC"},{"key":"5099472_CR22","volume-title":"Su Alcune Definizioni Deboli di Curvatura per Insiemi Non Orientati","author":"C. Mantegazza","year":"1993","unstructured":"Mantegazza, C. 1993. Su Alcune Definizioni Deboli di Curvatura per Insiemi Non Orientati. Ph.D. Thesis, Dept. of Mathematics, SNS Pisa, Italy."},{"key":"5099472_CR23","doi-asserted-by":"crossref","unstructured":"Moghaddam, B. and Pentland, A. 1995. Probabilistic visual learning for object detection. In Proc.IEEE Internat.Conf.on Comp.Vis., pp. 786\u2013793.","DOI":"10.1109\/ICCV.1995.466858"},{"issue":"1\u20133","key":"5099472_CR24","first-page":"169","volume":"1","author":"J.-M. Morel","year":"1988","unstructured":"Morel, J.-M. and Solimini, S. 1988. Segmentation of images by variational methods: A constructive approach. Revista Matematica de la Universidad Complutense de Madrid, 1(1\u20133):169\u2013182.","journal-title":"Revista Matematica de la Universidad Complutense de Madrid"},{"key":"5099472_CR25","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"Mumford, D. and Shah, J. 1989. Optimal approximations by piecewise smooth functions and associated variational problems. Comm.Pure Appl.Math., 42:577\u2013685.","journal-title":"Comm. Pure Appl. Math."},{"key":"5099472_CR26","series-title":"LNCS","first-page":"224","volume-title":"ECCV","author":"N. Paragios","year":"2000","unstructured":"Paragios, N. and Deriche, R. 2000. Coupled geodesic active regions for image segmentation: a level set approach. In ECCV, D. Vernon (Ed.), vol. 1843 of LNCS, Springer: Berlin, pp. 224\u2013240."},{"key":"5099472_CR27","first-page":"626","volume-title":"Advances in Neural Information Processing Systems 10","author":"S. Roweis","year":"1998","unstructured":"Roweis., S. EM algorithms for PCA and SPCA. 1998. In Advances in Neural Information Processing Systems 10, M. Jordan, M. Kearns, and S. Solla (Eds.), MIT Press: Cambridge, MA, pp. 626\u2013632."},{"key":"5099472_CR28","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/0734-189X(83)90020-8","volume":"24","author":"D. Terzopoulos","year":"1983","unstructured":"Terzopoulos, D. 1983. Multilevel computational processes for visual surface reconstruction. Comp.Vis., Graph., and Imag.Proc., 24:52\u201396.","journal-title":"Comp. Vis., Graph., and Imag. Proc."},{"key":"5099472_CR29","series-title":"Technical Report Woe","volume-title":"Probabilistic principal component analysis","author":"M.E. Tipping","year":"1997","unstructured":"Tipping, M.E. and Bishop, C.M. 1997. Probabilistic principal component analysis. Neural Computing Research Group, Aston University, UK, Technical Report Woe-19."},{"key":"5099472_CR30","volume-title":"Development of a multigrid algorithm for diffusion snakes","author":"F. Tischh\u00e4user","year":"2001","unstructured":"Tischh\u00e4user, F. 2001. Development of a multigrid algorithm for diffusion snakes. Diploma thesis Department of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany (in German)."},{"key":"5099472_CR31","unstructured":"Wang, Y. and Staib, L.H. 1998. Boundary finding with correspondence using statistical shape models. In Proc.Conf.Computer Vis.and Pattern Recog., Santa Barbara, CA, pp. 338\u2013345."},{"issue":"1","key":"5099472_CR32","first-page":"33","volume":"LXX","author":"J. Weickert","year":"2001","unstructured":"Weickert, J. 2001. Applications of nonlinear diffusion filtering in image processing and computer vision. Acta Mathematica Universitatis Comenianae, LXX(1):33\u201350.","journal-title":"Acta Mathematica Universitatis Comenianae"},{"issue":"8","key":"5099472_CR33","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1109\/34.400572","volume":"17","author":"M. Werman","year":"1995","unstructured":"Werman, M. and Weinshall, D. 1995. Similarity and affine invariant distances between 2d point sets. IEEE Trans.on Patt.Anal.and Mach.Intell., 17(8):810\u2013814.","journal-title":"IEEE Trans. on Patt. Anal. and Mach. Intell."},{"key":"5099472_CR34","volume-title":"An Introduction to Multigrid Methods","author":"P. Wesseling","year":"1992","unstructured":"Wesseling, P. 1992. An Introduction to Multigrid Methods. John Wiley: Chichester."},{"key":"5099472_CR35","doi-asserted-by":"crossref","unstructured":"Yezzi, A., Soatto, S., Tsai, A., and Willsky, A. 2002. The Mumford-Shah functional: From segmentation to stereo. Mathematics and Multimedia.","DOI":"10.1007\/978-1-4757-4127-8_8"},{"key":"5099472_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0377-0427(90)90252-U","volume":"33","author":"P.M. de Zeeuw","year":"1990","unstructured":"de Zeeuw, P.M. 1990. Matrix-dependent prolongations and restrictions in a blackbox multigrid solver. J.Comp.Appl.Math., 33:1\u201327.","journal-title":"J. Comp. Appl. Math."},{"issue":"11","key":"5099472_CR37","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1109\/34.632983","volume":"19","author":"S.C. Zhu","year":"1997","unstructured":"Zhu, S.C. and Mumford, D. 1997. Prior learning and Gibbs reaction\u2013diffusion. IEEE Trans.on Patt.Anal.and Mach.Intell., 19(11):1236\u20131250.","journal-title":"IEEE Trans. on Patt. Anal. and Mach. Intell."},{"issue":"9","key":"5099472_CR38","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1109\/34.537343","volume":"18","author":"S.C. Zhu","year":"1996","unstructured":"Zhu, S.C. and Yuille, A. 1996. Region competition: Unifying snakes, region growing, and Bayes\/MDL for multiband image segmentation. IEEE Trans.on Patt.Anal.and Mach.Intell., 18(9):884\u2013900.","journal-title":"IEEE Trans. on Patt. Anal. and Mach. Intell."}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1020826424915.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1020826424915\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1020826424915.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T09:28:41Z","timestamp":1754904521000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1020826424915"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["5099472"],"URL":"https:\/\/doi.org\/10.1023\/a:1020826424915","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}