{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:38:43Z","timestamp":1772293123163,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2-3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2013,2]]},"DOI":"10.1007\/s10915-012-9615-6","type":"journal-article","created":{"date-parts":[[2012,6,11]],"date-time":"2012-06-11T13:18:41Z","timestamp":1339420721000},"page":"513-530","source":"Crossref","is-referenced-by-count":3,"title":["Statistical Density Estimation Using Threshold Dynamics for Geometric Motion"],"prefix":"10.1007","volume":"54","author":[{"given":"Tijana","family":"Kosti\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Bertozzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,6,12]]},"reference":[{"key":"9615_CR1","volume-title":"Singularities and Similarities in Interface Flows, Trends and Perspectives in Applied Mathematics","author":"A.L. Bertozzi","year":"1994","unstructured":"Bertozzi, A.L., Brenner, M.P., Dupont, T.F., Kadanoff, L.P.: Singularities and Similarities in Interface Flows, Trends and Perspectives in Applied Mathematics. Springer, New York (1994)"},{"key":"9615_CR2","unstructured":"Brown, E.S., Chan, T.F., Bresson, X.: A convex relaxation method for a class of vector-valued minimization problems with applications to Mumford-Shah segmentation. Ucla cam report 10-43 (2010)"},{"issue":"1","key":"9615_CR3","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/TIP.2006.887728","volume":"16","author":"A.L. Bertozzi","year":"2007","unstructured":"Bertozzi, A.L., Esedoglu, S., Gillette, A.: Inpainting of binary images using the Cahn-Hilliard equation. IEEE Trans. Image Process. 16(1), 285\u2013291 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9615_CR4","first-page":"16","volume":"66","author":"T.F. Chan","year":"2006","unstructured":"Chan, T.F., Nikolova, M., Esedoglu, S.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66, 16\u201332 (2006)","journal-title":"SIAM J. Appl. Math."},{"key":"9615_CR5","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"2","author":"T.F. Chan","year":"2001","unstructured":"Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 2, 266 (2001)","journal-title":"IEEE Trans. Image Process."},{"issue":"6","key":"9615_CR6","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s00791-008-0113-1","volume":"12","author":"G. Chung","year":"2009","unstructured":"Chung, G., Vese, L.A.: Image segmentation using a multilayer level-set approach. Comput. Vis. Sci. 12(6), 267\u2013285 (2009)","journal-title":"Comput. Vis. Sci."},{"issue":"5","key":"9615_CR7","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1109\/TIP.2008.919367","volume":"17","author":"J.A. Dobrosotskaya","year":"2008","unstructured":"Dobrosotskaya, J.A., Bertozzi, A.L.: A\u00a0wavelet-Laplace variational technique for image deconvolution and inpainting. IEEE Trans. Image Process. 17(5), 657\u2013663 (2008)","journal-title":"IEEE Trans. Image Process."},{"key":"9615_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-0716-1244-6","volume-title":"Maximum Penalized Likelihood Estimation","author":"P.P.B. Eggermont","year":"2001","unstructured":"Eggermont, P.P.B., LaRiccia, N.V.: Maximum Penalized Likelihood Estimation. Springer, Berlin (2001)"},{"issue":"1","key":"9615_CR9","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/j.jcp.2005.05.027","volume":"211","author":"S. Esedoglu","year":"2006","unstructured":"Esedoglu, S., Tsai, Y.R.: Threshold dynamics for the piecewise constant Mumford-Shah functional. J.\u00a0Comput. Phys. 211(1), 367\u2013384 (2006)","journal-title":"J.\u00a0Comput. Phys."},{"issue":"1","key":"9615_CR10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1023\/A:1021837026373","volume":"18","author":"S. Esedoglu","year":"2003","unstructured":"Esedoglu, S., March, R.: Segmentation with depth but without detecting junctions. J. Math. Imaging Vis. 18(1), 7\u201315 (2003). Special issue on imaging science, 2002","journal-title":"J. Math. Imaging Vis."},{"issue":"4","key":"9615_CR11","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.jcp.2009.10.002","volume":"229","author":"S. Esedoglu","year":"2010","unstructured":"Esedoglu, S., Ruuth, S.J., Tsai, R.: Diffusion generated motion using signed distance functions. J. Comput. Phys. 229(4), 1017\u20131042 (2010)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9615_CR12","doi-asserted-by":"crossref","first-page":"263","DOI":"10.4171\/IFB\/189","volume":"10","author":"S. Esedoglu","year":"2008","unstructured":"Esedoglu, S., Ruuth, S.J., Tsai, R.: Threshold dynamics for high order geometric motions. Interfaces Free Bound. 10(3), 263\u2013282 (2008)","journal-title":"Interfaces Free Bound."},{"key":"9615_CR13","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1098\/rsta.1922.0009","volume":"222","author":"R.A. Fisher","year":"1922","unstructured":"Fisher, R.A.: On the mathematical foundations of theoretical statistics. Philos. Trans. R. Soc. Lond. A 222, 309\u2013360 (1922)","journal-title":"Philos. Trans. R. Soc. Lond. A"},{"issue":"10","key":"9615_CR14","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1109\/TIP.2005.852200","volume":"14","author":"S. Gao","year":"2005","unstructured":"Gao, S., Bui, T.D.: Image segmentation and selective smoothing by using Mumford-Shah model. IEEE Trans. Image Process. 14(10), 1537\u20131549 (2005)","journal-title":"IEEE Trans. Image Process."},{"issue":"2","key":"9615_CR15","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T. Goldstein","year":"2009","unstructured":"Goldstein, T., Osher, S.: The split Bregman method for L 1-regularized problems. SIAM J. Imaging Sci. 2(2), 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"9615_CR16","volume-title":"Proceedings of the 4th Annual Hawaii International Conference on Statistics","author":"F. Gibou","year":"2005","unstructured":"Gibou, F., Fedkiw, R.: A\u00a0fast hybrid k-means level set algorithm for segmentation. In: Proceedings of the 4th Annual Hawaii International Conference on Statistics (2005)"},{"issue":"6","key":"9615_CR17","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s00791-008-0113-1","volume":"12","author":"G. Chung","year":"2009","unstructured":"Chung, G., Vese, L.A.: Image segmentation using a multilayer level-set approach. Comput. Vis. Sci. 12(6), 267\u2013285 (2009)","journal-title":"Comput. Vis. Sci."},{"key":"9615_CR18","first-page":"613","volume-title":"Advances in Statistical Modeling and Inference, Essays in Honor of Kjell A. Doksum","author":"R. Koenker","year":"2006","unstructured":"Koenker, R., Mizera, I.: Density estimation by total variation regularization. In: Advances in Statistical Modeling and Inference, Essays in Honor of Kjell A. Doksum, pp.\u00a0613\u2013634. World Scientific, Singapore (2006)"},{"issue":"1\u20132","key":"9615_CR19","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1017\/S0308210500025026","volume":"111","author":"R.V. Kohn","year":"1989","unstructured":"Kohn, R.V., Sternberg, P.: Local minimisers and singular perturbations. Proc. R. Soc. Edinb. A 111(1\u20132), 69\u201384 (1989)","journal-title":"Proc. R. Soc. Edinb. A"},{"key":"9615_CR20","series-title":"AMS Selection in Math.","first-page":"73","volume-title":"The Computational Crystal Growers","author":"B. Merriman","year":"1992","unstructured":"Merriman, B., Bence, J., Osher, S.: Diffusion generated motion by mean curvature. In: The Computational Crystal Growers. AMS Selection in Math., pp.\u00a073\u201383 (1992)"},{"issue":"2","key":"9615_CR21","doi-asserted-by":"crossref","first-page":"2267","DOI":"10.1016\/j.jcp.2007.03.034","volume":"225","author":"B. Merriman","year":"2007","unstructured":"Merriman, B., Ruuth, S.J.: Diffusion generated motion of curves on surfaces. J.\u00a0Comput. Phys. 225(2), 2267\u20132282 (2007)","journal-title":"J.\u00a0Comput. Phys."},{"issue":"2","key":"9615_CR22","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1198\/jcgs.2010.09048","volume":"20","author":"G. Mohler","year":"2011","unstructured":"Mohler, G., Bertozzi, A., Goldstein, T., Osher, S.: Fast TV regularization for 2D maximum penalized likelihood estimation. J. Comput. Graph. Stat. 20(2), 479 (2011)","journal-title":"J. Comput. Graph. Stat."},{"key":"9615_CR23","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577\u2013658 (1989)","journal-title":"Commun. Pure Appl. Math."},{"key":"9615_CR24","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S. Osher","year":"1988","unstructured":"Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J.\u00a0Comput. Phys. 79, 12\u201349 (1988)","journal-title":"J.\u00a0Comput. Phys."},{"issue":"1","key":"9615_CR25","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1137\/0149007","volume":"49","author":"J. Rubinstein","year":"1989","unstructured":"Rubinstein, J., Sternberg, P., Keller, J.B.: Fast reaction, slow diffusion, and curve shortening. SIAM J. Appl. Math. 49(1), 116\u2013133 (1989)","journal-title":"SIAM J. Appl. Math."},{"key":"9615_CR26","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1006\/jcph.1998.6025","volume":"144","author":"S.J. Ruuth","year":"1998","unstructured":"Ruuth, S.J.: Efficient algorithms for diffusion-generated motion by mean curvature. J. Comput. Phys. 144, 603\u2013625 (1998)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9615_CR27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1111\/j.1467-9469.2009.00672.x","volume":"37","author":"S. Sardy","year":"2010","unstructured":"Sardy, S., Tseng, P.: Density estimation by total variation penalized likelihood driven by the sparsity l1 information criterion. Scand. J. Stat. 37(2), 321\u2013337 (2010)","journal-title":"Scand. J. Stat."},{"key":"9615_CR28","doi-asserted-by":"crossref","unstructured":"Smith, L., Keegan, M., Wittman, T., Mohler, G., Bertozzi, A.: Improving density estimation by incorporating spatial information. URASIP J. Adv. Signal Process. 2010","DOI":"10.1155\/2010\/265631"},{"issue":"3","key":"9615_CR29","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1020874308076","volume":"50","author":"L.A. Vese","year":"2002","unstructured":"Vese, L.A., Chan, T.F.: A\u00a0multiphase level set framework for image segmentation using the mumford and shah model. Int. J. Comput. Vis. 50(3), 271\u2013293 (2002)","journal-title":"Int. J. Comput. Vis."},{"key":"9615_CR30","unstructured":"Song, B., Chan, T.: A\u00a0fast algorithm for level set based optimization. UCLA"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-012-9615-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T09:44:31Z","timestamp":1642412671000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-012-9615-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,12]]},"references-count":30,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["9615"],"URL":"https:\/\/doi.org\/10.1007\/s10915-012-9615-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,12]]}}}