{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:37:24Z","timestamp":1761964644076,"version":"3.41.0"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319184609"},{"type":"electronic","value":"9783319184616"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-18461-6_37","type":"book-chapter","created":{"date-parts":[[2015,4,27]],"date-time":"2015-04-27T05:55:20Z","timestamp":1430114120000},"page":"461-473","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["PDE-Based Color Morphology Using Matrix Fields"],"prefix":"10.1007","author":[{"given":"Ali Sharifi","family":"Boroujerdi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Breu\u00df","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernhard","family":"Burgeth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Kleefeld","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,4,28]]},"reference":[{"key":"37_CR1","volume-title":"Computer Graphics and Geometric Modeling: Implementation and Algorithms","author":"MK Agoston","year":"2005","unstructured":"Agoston, M.K.: Computer Graphics and Geometric Modeling: Implementation and Algorithms. Springer, London (2005)"},{"key":"37_CR2","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 in image processing. Archive for Rational Mechanics and Analysis 123, 199\u2013257 (1993)","journal-title":"Archive for Rational Mechanics and Analysis"},{"issue":"11","key":"37_CR3","doi-asserted-by":"publisher","first-page":"2914","DOI":"10.1016\/j.patcog.2007.02.004","volume":"40","author":"E Aptoula","year":"2007","unstructured":"Aptoula, E., Lef\u00e8vre, S.: A Comparative Study on Multivariate Mathematical Morphology. Pattern Recognition 40(11), 2914\u20132929 (2007)","journal-title":"Pattern Recognition"},{"key":"37_CR4","doi-asserted-by":"crossref","unstructured":"Arehart, A.B., Vincent, L., Kimia, B.B.: Mathematical morphology: The Hamilton-Jacobi connection. In: Proc. Fourth International Conference on Computer Vision pp. 215\u2013219 (1993)","DOI":"10.1109\/ICCV.1993.378217"},{"issue":"2","key":"37_CR5","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10851-006-9696-7","volume":"25","author":"M Breu\u00df","year":"2006","unstructured":"Breu\u00df, M., Weickert, J.: A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion. Journal of Mathematical Imaging and Vision 25(2), 187\u2013201 (2006)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"37_CR6","doi-asserted-by":"crossref","unstructured":"Brockett, R.W., Maragos, P.: Evolution equations for continuous-scale morphology, In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing vol. 3, 125\u2013128 (1992)","DOI":"10.1109\/ICASSP.1992.226260"},{"key":"37_CR7","doi-asserted-by":"crossref","unstructured":"Burgeth, B., Breu\u00df, M., Didas, S., Weickert, J.: PDE-based Morphology for Matrix Fields: Numerical Solution Schemes, Tensors in Image Processing and Computer Vision, pp. 125\u2013150 (2009)","DOI":"10.1007\/978-1-84882-299-3_6"},{"issue":"4","key":"37_CR8","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1016\/j.imavis.2006.06.002","volume":"25","author":"B Burgeth","year":"2007","unstructured":"Burgeth, B., Bruhn, A., Didas, S., Weickert, J., Welk, M.: Morphology for tensor data: ordering versus PDE-based approach. Image and Vision Computing 25(4), 496\u2013511 (2007)","journal-title":"Image and Vision Computing"},{"key":"37_CR9","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.patrec.2014.01.018","volume":"47","author":"B Burgeth","year":"2014","unstructured":"Burgeth, B., Kleefeld, A.: An approach to color-morphology based on Einstein addition and Loewner order. Pattern Recognition Letters 47, 29\u201339 (2014)","journal-title":"Pattern Recognition Letters"},{"issue":"3","key":"37_CR10","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1117\/1.482677","volume":"8","author":"ML Comer","year":"1999","unstructured":"Comer, M.L., Delp, E.J.: Morphological operations for color image processing. J. Electron. Imaging 8(3), 279\u2013289 (1999)","journal-title":"J. Electron. Imaging"},{"key":"37_CR11","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1006\/cviu.1995.1058","volume":"62","author":"J Goutsias","year":"1995","unstructured":"Goutsias, J., Heijmans, H.J.A.M., Sivakumar, K.: Morphological operators for image sequences. Computer Vision and Image Understanding 62, 326\u2013346 (1995)","journal-title":"Computer Vision and Image Understanding"},{"key":"37_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/978-3-642-38294-9_23","volume-title":"Mathematical Morphology and Its Applications to Signal and Image Processing","author":"Jasper J van de Gronde","year":"2013","unstructured":"van de Gronde, Jasper J., Roerdink, Jos B.T.M.: Group-invariant frames for colour morphology. In: Hendriks, Cris LLuengo, Borgefors, Gunilla, Strand, Robin (eds.) ISMM 2013. LNCS, vol. 7883, pp. 267\u2013278. Springer, Heidelberg (2013)"},{"issue":"4","key":"37_CR13","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1109\/TPAMI.1987.4767941","volume":"9","author":"RM Haralick","year":"1987","unstructured":"Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology. IEEE Trans. Pattern Anal, Machine Intell 9(4), 532\u2013550 (1987)","journal-title":"IEEE Trans. Pattern Anal, Machine Intell"},{"key":"37_CR14","unstructured":"Matheron, G.: El\u00e9ments Pour une Thorie des Milieux Poreux. Masson, Paris (1967)"},{"key":"37_CR15","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 Journal on Numerical Analysis 27, 919\u2013940 (1990)","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"37_CR16","doi-asserted-by":"publisher","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. of Computational Physics 79, 12\u201349 (1988)","journal-title":"J. of Computational Physics"},{"key":"37_CR17","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1137\/0729053","volume":"29","author":"E Rouy","year":"1992","unstructured":"Rouy, E., Tourin, A.: A viscosity solutions approach to shape-from-shading. SIAM Journal on Numerical Analysis 29, 867\u2013884 (1992)","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"37_CR18","doi-asserted-by":"crossref","unstructured":"G. Sapiro, Geometric Partial Differential Equations and Image Analysis, pp. 96\u2013102. Cambridge University Press (2001)","DOI":"10.1017\/CBO9780511626319"},{"key":"37_CR19","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.1016\/0031-3203(93)90142-J","volume":"26","author":"G Sapiro","year":"1993","unstructured":"Sapiro, G., Kimmel, R., Shaked, D., Kimia, B.B., Bruckstein, A.M.: Implementing continuous-scale morphology via curve evolution. Pattern Recognition 26, 1363\u20131372 (1993)","journal-title":"Pattern Recognition"},{"key":"37_CR20","unstructured":"Serra, J.: \u00c9chantillonnage et estimation des ph\u00e9nom\u00e8nes de transition minier, Ph.D thesis, University of Nancy, France (1967)"},{"key":"37_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/978-3-642-03613-2_2","volume-title":"Mathematical Morphology and Its Application to Signal and Image Processing","author":"Jean Serra","year":"2009","unstructured":"Serra, Jean: The \u201cFalse Colour\u201d problem. In: Wilkinson, Michael H.F., Roerdink, Jos B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 13\u201323. Springer, Heidelberg (2009)"},{"key":"37_CR22","unstructured":"van den Boomgaard, R.: Mathematical Morphology: Extensions Towards Computer Vision, Ph.D thesis, University of Amsterdam, The Netherlands (1992)"},{"issue":"2","key":"37_CR23","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/0734-189X(89)90131-X","volume":"45","author":"LJ van Vliet","year":"1989","unstructured":"van Vliet, L.J., Young, I.T., Beckers, A.L.D.: A nonlinear Laplace operator as edge detector in noisy images. Computer Vision, Graphics and Image Processing 45(2), 167\u2013195 (1989)","journal-title":"Computer Vision, Graphics and Image Processing"}],"container-title":["Lecture Notes in Computer Science","Scale Space and Variational Methods in Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-18461-6_37","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T15:20:22Z","timestamp":1748359222000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-18461-6_37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319184609","9783319184616"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-18461-6_37","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"28 April 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}