{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T22:28:27Z","timestamp":1791152907192,"version":"4.1.0"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319187198","type":"print"},{"value":"9783319187204","type":"electronic"}],"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":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-18720-4_30","type":"book-chapter","created":{"date-parts":[[2015,5,15]],"date-time":"2015-05-15T03:28:14Z","timestamp":1431660494000},"page":"351-362","source":"Crossref","is-referenced-by-count":5,"title":["Sponges for Generalized Morphology"],"prefix":"10.1007","author":[{"given":"Jasper J.","family":"van de Gronde","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos B. T. M.","family":"Roerdink","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"30_CR1","doi-asserted-by":"crossref","unstructured":"Angulo, J.: Supremum\/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matrices. In: Nielsen, F., Bhatia, R. (eds.) Matrix Information Geometry, pp. 3\u201333. Springer, Heidelberg (2013)","DOI":"10.1007\/978-3-642-30232-9_1"},{"key":"30_CR2","doi-asserted-by":"crossref","unstructured":"Angulo, J., Lef\u00e8vre, S., Lezoray, O.: Color Representation and Processing in Polar Color Spaces. In: Fernandez-Maloigne, C., Robert-Inacio, F., Macaire, L. (eds.) Digital Color Imaging, chap. 1, pp. 1\u201340. John Wiley & Sons, Inc., Hoboken (2012)","DOI":"10.1002\/9781118561966.ch1"},{"key":"30_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/978-3-642-40020-9_59","volume-title":"Geometric Science of Information","author":"J. Angulo","year":"2013","unstructured":"Angulo, J., Velasco-Forero, S.: Complete Lattice Structure of Poincar\u00e9 Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2013. LNCS, vol.\u00a08085, pp. 535\u2013542. Springer, Heidelberg (2013)"},{"issue":"9","key":"30_CR4","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1016\/j.imavis.2008.12.007","volume":"27","author":"E. Aptoula","year":"2009","unstructured":"Aptoula, E., Lef\u00e8vre, S.: On the morphological processing of hue. Image Vis. Comput.\u00a027(9), 1394\u20131401 (2009)","journal-title":"Image Vis. Comput."},{"issue":"4","key":"30_CR5","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1109\/5.54807","volume":"78","author":"J. Astola","year":"1990","unstructured":"Astola, J., Haavisto, P., Neuvo, Y.: Vector median filters. Proc. IEEE\u00a078(4), 678\u2013689 (1990)","journal-title":"Proc. IEEE"},{"issue":"4","key":"30_CR6","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 matrix data: Ordering versus PDE-based approach. Image Vis. Comput.\u00a025(4), 496\u2013511 (2007)","journal-title":"Image Vis. Comput."},{"key":"30_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/978-3-642-38294-9_21","volume-title":"Mathematical Morphology and Its Applications to Signal and Image Processing","author":"B. Burgeth","year":"2013","unstructured":"Burgeth, B., Kleefeld, A.: Morphology for Color Images via Loewner Order for Matrix Fields. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds.) ISMM 2013. LNCS, vol.\u00a07883, pp. 243\u2013254. Springer, Heidelberg (2013)"},{"key":"30_CR8","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 Recognit. Lett.\u00a047, 29\u201339 (2014)","journal-title":"Pattern Recognit. Lett."},{"key":"30_CR9","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/1-4020-3443-1_37","volume-title":"Mathematical Morphology: 40 Years On, Computational Imaging and Vision","author":"B. Burgeth","year":"2005","unstructured":"Burgeth, B., Papenberg, N., Bruhn, A., Welk, M., Feddern, C., Weickert, J.: Morphology for Higher-Dimensional Tensor Data Via Loewner Ordering. In: Ronse, C., Najman, L., Decenci\u00e8re, E. (eds.) Mathematical Morphology: 40 Years On, Computational Imaging and Vision, vol.\u00a030, pp. 407\u2013416. Springer, Netherlands (2005)"},{"key":"30_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/978-3-540-24673-2_13","volume-title":"Computer Vision - ECCV 2004","author":"B. Burgeth","year":"2004","unstructured":"Burgeth, B., Welk, M., Feddern, C., Weickert, J.: Morphological Operations on Matrix-Valued Images. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol.\u00a03024, pp. 155\u2013167. Springer, Heidelberg (2004)"},{"key":"30_CR11","series-title":"Math. Vis","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/3-540-31272-2_22","volume-title":"Visualization and Processing of Tensor Fields","author":"B. Burgeth","year":"2006","unstructured":"Burgeth, B., Welk, M., Feddern, C., Weickert, J.: Mathematical Morphology on Tensor Data Using the Loewner Ordering. In: Weickert, J., Hagen, H. (eds.) Visualization and Processing of Tensor Fields. Math. Vis, pp. 357\u2013368. Springer, Heidelberg (2006)"},{"key":"30_CR12","unstructured":"Chevallier, E., Angulo, J.: Optimized total order for mathematical morphology on metric spaces. Tech. rep., Centre de Morphologie Math\u00e9matique, MINES ParisTech (2014)"},{"key":"30_CR13","first-page":"93","volume":"16","author":"E. Fried","year":"1973","unstructured":"Fried, E.: Weakly associative lattices with join and meet of several elements. Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math.\u00a016, 93\u201398 (1973)","journal-title":"Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math."},{"issue":"1","key":"30_CR14","doi-asserted-by":"publisher","first-page":"59","DOI":"10.2140\/pjm.1973.49.59","volume":"49","author":"E. Fried","year":"1973","unstructured":"Fried, E., Gr\u00e4tzer, G.: A nonassociative extension of the class of distributive lattices. Pacific J. Math.\u00a049(1), 59\u201378 (1973)","journal-title":"Pacific J. Math."},{"key":"30_CR15","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4064\/cm-27-2-215-221","volume":"27","author":"E. Fried","year":"1973","unstructured":"Fried, E., Gr\u00e4tzer, G.: Some examples of weakly associative lattices. Colloq. Math.\u00a027, 215\u2013221 (1973)","journal-title":"Colloq. Math."},{"issue":"4","key":"30_CR16","first-page":"501","volume":"2","author":"E. Fried","year":"1976","unstructured":"Fried, E., Gr\u00e4tzer, G.: Partial and free weakly associative lattices. Houston J. Math.\u00a02(4), 501\u2013512 (1976)","journal-title":"Houston J. Math."},{"key":"30_CR17","doi-asserted-by":"crossref","unstructured":"Gomila, C., Meyer, F.: Levelings in vector spaces. In: Int. Conf. Image Proc., vol.\u00a02, pp. 929\u2013933. IEEE (1999)","DOI":"10.1109\/ICIP.1999.823034"},{"key":"30_CR18","unstructured":"Gr\u00e4tzer, G.: General Lattice Theory, 2nd edn. Birkh\u00e4user Verlag (2003)"},{"key":"30_CR19","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.patrec.2014.03.013","volume":"47","author":"J.J. van de Gronde","year":"2014","unstructured":"van de Gronde, J.J., Roerdink, J.B.T.M.: Frames, the Loewner order and eigendecomposition for morphological operators on tensor fields. Pattern Recognit. Lett.\u00a047, 40\u201349 (2014)","journal-title":"Pattern Recognit. Lett."},{"issue":"3","key":"30_CR20","doi-asserted-by":"publisher","first-page":"1276","DOI":"10.1109\/TIP.2014.2300816","volume":"23","author":"J.J. van de Gronde","year":"2014","unstructured":"van de Gronde, J.J., Roerdink, J.B.T.M.: Group-Invariant Colour Morphology Based on Frames. IEEE Trans. Image Process.\u00a023(3), 1276\u20131288 (2014)","journal-title":"IEEE Trans. Image Process."},{"issue":"12","key":"30_CR21","doi-asserted-by":"publisher","first-page":"1842","DOI":"10.1109\/83.974569","volume":"10","author":"A.G. Hanbury","year":"2001","unstructured":"Hanbury, A.G., Serra, J.: Morphological operators on the unit circle. IEEE Trans. Image Process.\u00a010(12), 1842\u20131850 (2001)","journal-title":"IEEE Trans. Image Process."},{"key":"30_CR22","unstructured":"Heijmans, H.J.A.M.: Morphological image operators. Academic Press (1994)"},{"issue":"1","key":"30_CR23","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1007\/BF01191789","volume":"16","author":"K. Leutola","year":"1983","unstructured":"Leutola, K., Nieminen, J.: Posets and generalized lattices. Algebra Universalis\u00a016(1), 344\u2013354 (1983)","journal-title":"Algebra Universalis"},{"issue":"3","key":"30_CR24","doi-asserted-by":"publisher","first-page":"2190","DOI":"10.1016\/j.neuroimage.2009.10.071","volume":"49","author":"O. Pasternak","year":"2010","unstructured":"Pasternak, O., Sochen, N., Basser, P.J.: The effect of metric selection on the analysis of diffusion tensor MRI data. NeuroImage\u00a049(3), 2190\u20132204 (2010)","journal-title":"NeuroImage"},{"key":"30_CR25","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1117\/12.271144","volume":"3026","author":"R.A. Peters","year":"1997","unstructured":"Peters, R.A.: Mathematical morphology for angle-valued images. Proceedings of the SPIE\u00a03026, 84\u201394 (1997)","journal-title":"Proceedings of the SPIE"},{"issue":"1","key":"30_CR26","first-page":"5","volume":"18","author":"J. Rach\u016fnek","year":"1979","unstructured":"Rach\u016fnek, J.: Semi-ordered groups. Sborn\u00edk prac\u00ed P\u0159\u00edrodov\u011bdeck\u00e9 fakulty University Palack\u00e9ho v Olomouci. Matematika\u00a018(1), 5\u201320 (1979)","journal-title":"Matematika"},{"key":"30_CR27","doi-asserted-by":"crossref","unstructured":"Serra, J.: Anamorphoses and function lattices. In: Dougherty, E.R., Gader, P.D., Serra, J.C. (eds.) Image Algebra and Morphological Image Processing IV, vol.\u00a02030, pp. 2\u201311. SPIE Proceedings (1993)","DOI":"10.1117\/12.146650"},{"issue":"1","key":"30_CR28","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1007\/BF02944982","volume":"1","author":"H.L. Skala","year":"1971","unstructured":"Skala, H.L.: Trellis theory. Algebra Universalis\u00a01(1), 218\u2013233 (1971)","journal-title":"Algebra Universalis"},{"key":"30_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/978-3-540-72849-8_59","volume-title":"Pattern Recognition and Image Analysis","author":"M.C. Tobar","year":"2007","unstructured":"Tobar, M.C., Platero, C., Gonz\u00e1lez, P.M., Asensio, G.: Mathematical morphology in the HSI colour space. In: Mart\u00ed, J., Bened\u00ed, J.M., Mendon\u00e7a, A.M., Serrat, J. (eds.) IbPRIA 2007. LNCS, vol.\u00a04478, pp. 467\u2013474. Springer, Heidelberg (2007)"},{"key":"30_CR30","unstructured":"Zanoguera, F., Meyer, F.: On the implementation of non-separable vector levelings. In: Talbot, H., Beare, R. (eds.) Mathematical Morphology, p. 369. CSIRO Publishing (2002)"}],"container-title":["Lecture Notes in Computer Science","Mathematical Morphology and Its Applications to Signal and Image Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-18720-4_30","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T00:09:29Z","timestamp":1748390969000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-18720-4_30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319187198","9783319187204"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-18720-4_30","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}