{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T17:55:30Z","timestamp":1725558930791},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540255475"},{"type":"electronic","value":"9783540320128"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11408031_26","type":"book-chapter","created":{"date-parts":[[2010,7,13]],"date-time":"2010-07-13T14:04:57Z","timestamp":1279029897000},"page":"303-315","source":"Crossref","is-referenced-by-count":4,"title":["A Non-convex PDE Scale Space"],"prefix":"10.1007","author":[{"given":"Markus","family":"Grasmair","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Lenzen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Obereder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otmar","family":"Scherzer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Fuchs","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"26_CR1","volume-title":"Nonlinear Functional Analysis and its Applications I","author":"E. Zeidler","year":"1993","unstructured":"Zeidler, E.: Nonlinear Functional Analysis and its Applications I. Springer, New York (1993) (corrected printing)"},{"key":"26_CR2","doi-asserted-by":"publisher","first-page":"265","DOI":"10.2307\/2373376","volume":"93","author":"M.G. Crandall","year":"1971","unstructured":"Crandall, M.G., Liggett, T.M.: Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math.\u00a093, 265\u2013298 (1971)","journal-title":"Amer. J. Math."},{"key":"26_CR3","doi-asserted-by":"crossref","unstructured":"Radmoser, E., Scherzer, O., Weickert, J.: Scale-space properties of regularization methods. In: [29] (1999)","DOI":"10.1007\/3-540-48236-9_19"},{"key":"26_CR4","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1023\/A:1008344608808","volume":"12","author":"O. Scherzer","year":"2000","unstructured":"Scherzer, O., Weickert, J.: Relations between regularization and diffusion filtering. J. Math. Imag. Vision\u00a012, 43\u201363 (2000)","journal-title":"J. Math. Imag. Vision"},{"key":"26_CR5","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1006\/jvci.1999.0437","volume":"11","author":"E. Radmoser","year":"2000","unstructured":"Radmoser, E., Scherzer, O., Weickert, J.: Scale-space properties of nonstationary iterative regularization methods. Journal of Visual Communication and Image Representation\u00a011, 96\u2013114 (2000)","journal-title":"Journal of Visual Communication and Image Representation"},{"key":"26_CR6","doi-asserted-by":"crossref","unstructured":"Mr\u00e1zek, P., Weickert, J., Steidl, G.: Correspondences between wavelet shrinkage and nonlinear diffusion. In: [30], pp. 101\u2013116 (2003)","DOI":"10.1007\/3-540-44935-3_8"},{"key":"26_CR7","doi-asserted-by":"crossref","unstructured":"Steidl, G., Weickert, J.: Relations between soft wavelet shrinkage and total variation denoising. In: [31], pp. 198\u2013205 (2002)","DOI":"10.1007\/3-540-45783-6_25"},{"key":"26_CR8","series-title":"Lecture Notes in Math","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1007\/BFb0094296","volume-title":"Viscosity solutions and applications (Montecatini Terme, 1995)","author":"L.C. Evans","year":"1997","unstructured":"Evans, L.C.: Regularity for fully nonlinear elliptic equations and motion by mean curvature. In: Viscosity solutions and applications (Montecatini Terme, 1995). Lecture Notes in Math., vol.\u00a01660, pp. 98\u2013133. Springer, Berlin (1997)"},{"key":"26_CR9","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/BF00375127","volume":"123","author":"L. Alvarez","year":"1993","unstructured":"Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axioms and fundamental equations of image processing. Arch. Ration. Mech. Anal.\u00a0123, 199\u2013257 (1993)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"26_CR10","doi-asserted-by":"crossref","unstructured":"Scherzer, O.: Explicit versus implicit relative error regularization on the space of functions of bounded variation. In: [32], pp. 171\u2013198 (2002)","DOI":"10.1090\/conm\/313\/05376"},{"key":"26_CR11","unstructured":"Lenzen, F., Scherzer, O.: Tikhonov type regularization methods: history and recent progress. In: Proceeding Eccomas 2004 (2004)"},{"key":"26_CR12","unstructured":"Grasmair, M., Scherzer, O.: Relaxation of non-convex singular functionals (2004) (submitted)"},{"key":"26_CR13","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/S0362-546X(99)00413-7","volume":"45","author":"O. Scherzer","year":"2001","unstructured":"Scherzer, O.: A posteriori error estimates for nonlinear ill\u2013posed problems. Nonlinear Analysis\u00a045, 459\u2013481 (2001)","journal-title":"Nonlinear Analysis"},{"key":"26_CR14","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1137\/0727053","volume":"27","author":"S. Osher","year":"1990","unstructured":"Osher, S., Rudin, L.I.: Feature-oriented image enhancement using shock filters. SIAM J. Numer. Anal.\u00a027, 919\u2013940 (1990)","journal-title":"SIAM J. Numer. Anal."},{"key":"26_CR15","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L. Rudin","year":"1992","unstructured":"Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D\u00a060, 259\u2013268 (1992)","journal-title":"Physica D"},{"key":"26_CR16","volume-title":"Measure Theory and Fine Properties of Functions","author":"L. Evans","year":"1992","unstructured":"Evans, L., Gariepy, R.: Measure Theory and Fine Properties of Functions. CRC\u2013Press, Boca Raton (1992)"},{"key":"26_CR17","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of bounded variation and free discontinuity problems","author":"L. Ambrosio","year":"2000","unstructured":"Ambrosio, L., Fusco, N., Pallara, D.: Functions of bounded variation and free discontinuity problems. The Clarendon Press Oxford University Press, New York (2000)"},{"key":"26_CR18","unstructured":"Temam, R.: Probl\u00e8mes math\u00e9matiques en plasticit\u00e9. In: M\u00e9thodes Math\u00e9matiques de l\u2019Informatique [Mathematical Methods of Information Science]. Gauthier-Villars, Montrouge, vol. 12 (1983)"},{"key":"26_CR19","volume-title":"Real and Complex Analysis","author":"W. Rudin","year":"1987","unstructured":"Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw-Hill, New York (1987)","edition":"3"},{"key":"26_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-51440-1","volume-title":"Direct Methods in the Calculus of Variations","author":"B. Dacorogna","year":"1989","unstructured":"Dacorogna, B.: Direct Methods in the Calculus of Variations. Springer, Berlin (1989)"},{"key":"26_CR21","volume-title":"Pure and Applied Mathematics","author":"A.W. Roberts","year":"1973","unstructured":"Roberts, A.W., Varberg, D.E.: Convex functions. In: Pure and Applied Mathematics, vol.\u00a057. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York (1973)"},{"key":"26_CR22","unstructured":"Grasmair, M., Scherzer, O.: Relaxation of nonlocal variational functionals (2004) (submitted)"},{"key":"26_CR23","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s002050050124","volume":"145","author":"G. Bouchitt\u00e9","year":"1998","unstructured":"Bouchitt\u00e9, G., Fonseca, I., Mascarenhas, L.: A global method for relaxation. Arch. Rational Mech. Anal.\u00a0145, 51\u201398 (1998)","journal-title":"Arch. Rational Mech. Anal."},{"key":"26_CR24","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/BF02797684","volume":"37","author":"G. Buttazzo","year":"1980","unstructured":"Buttazzo, G., Dal Maso, G.: \u0393-limits of integral functionals. J. Analyse Math.\u00a037, 145\u2013185 (1980)","journal-title":"J. Analyse Math."},{"key":"26_CR25","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/BF00380769","volume":"115","author":"P. Aviles","year":"1991","unstructured":"Aviles, P., Giga, Y.: Variational integrals on mappings of bounded variation and their lower semicontinuity. Arch. Ration. Mech. Anal.\u00a0115, 201\u2013255 (1991)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"26_CR26","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1137\/0523060","volume":"23","author":"I. Fonseca","year":"1992","unstructured":"Fonseca, I., M\u00fcller, S.: Quasi-convex integrands and lower semicontinuity in L 1. SIAM J. Math. Anal.\u00a023, 1081\u20131098 (1992)","journal-title":"SIAM J. Math. Anal."},{"key":"26_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF00386367","volume":"123","author":"I. Fonseca","year":"1993","unstructured":"Fonseca, I., M\u00fcller, S.: Relaxation of quasiconvex functionals in BV(\u03a9, R p ) for integrands $f(x, u, \\nabla u)$ . Arch. Ration. Mech. Anal.\u00a0123, 1\u201349 (1993)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"26_CR28","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s002110050166","volume":"72","author":"K. Deckelnick","year":"1995","unstructured":"Deckelnick, K., Dziuk, G.: Convergence of a finite element method for non-parametric mean curvature flow. Numer. Math.\u00a072, 197\u2013222 (1995)","journal-title":"Numer. Math."},{"key":"26_CR29","series-title":"Lecture Notes in Computer Science","volume-title":"Scale-Space 1999","year":"1999","unstructured":"Nielsen, M., Johansen, P., Olsen, O., Weickert, J. (eds.): Scale-Space 1999. LNCS, vol.\u00a01683. Springer, Heidelberg (1999)"},{"key":"26_CR30","series-title":"Lecture Notes in Computer Science","volume-title":"Scale Space Methods in Computer Vision","year":"2003","unstructured":"Griffin, L.D., Lillholm, M. (eds.): Scale-Space 2003. LNCS, vol.\u00a02695. Springer, Heidelberg (2003)"},{"key":"26_CR31","series-title":"Lecture Notes in Computer Science","volume-title":"Pattern Recognition","year":"2002","unstructured":"Van Gool, L. (ed.): DAGM 2002. LNCS, vol.\u00a02449. Springer, Heidelberg (2002)"},{"volume-title":"Interactions on Inverse Problems and Imaging. Contemporary Mathematics","year":"2002","key":"26_CR32","unstructured":"Nashed, M., Scherzer, O. (eds.): Interactions on Inverse Problems and Imaging. Contemporary Mathematics, vol.\u00a0313. AMS, Providence (2002)"}],"container-title":["Lecture Notes in Computer Science","Scale Space and PDE Methods in Computer Vision"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11408031_26.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T08:19:57Z","timestamp":1711613997000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11408031_26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540255475","9783540320128"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/11408031_26","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}