{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:38:22Z","timestamp":1761964702298},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,11,5]],"date-time":"2015-11-05T00:00:00Z","timestamp":1446681600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1007\/s10851-015-0607-7","type":"journal-article","created":{"date-parts":[[2015,11,5]],"date-time":"2015-11-05T19:26:43Z","timestamp":1446751603000},"page":"344-357","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["The Irregularity Issue of Total Orders on Metric Spaces and Its Consequences for Mathematical Morphology"],"prefix":"10.1007","volume":"54","author":[{"given":"Emmanuel","family":"Chevallier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Angulo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,11,5]]},"reference":[{"key":"607_CR1","volume-title":"Random Sets and Integral Geometry","author":"G Matheron","year":"1975","unstructured":"Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)"},{"key":"607_CR2","volume-title":"Image Analysis and Mathematical Morphology","author":"J Serra","year":"1988","unstructured":"Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1988)"},{"key":"607_CR3","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0734-189X(90)90148-O","volume":"50","author":"HJAM Heijmans","year":"1990","unstructured":"Heijmans, H.J.A.M., Ronse, C.: The algebraic basis of mathematical morphology\u2014part I: Dilations and erosions. Comput. Vis. Graph. Image Process. 50, 245\u2013295 (1990)","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"607_CR4","unstructured":"Serra, J.: Image Analysis and Mathematical Morphology. Vol II: Theoretical Advances. Academic Press, London (1988)"},{"key":"607_CR5","first-page":"483","volume-title":"Mathematical Morphology in Image Processing","author":"J Serra","year":"1992","unstructured":"Serra, J.: Anamorphoses and function lattices. In: Dougherty, (ed.) Mathematical Morphology in Image Processing, pp. 483\u2013523. Marcel Dekker, New York (1992)"},{"key":"607_CR6","doi-asserted-by":"crossref","unstructured":"Burgeth, B., Kleefeld, A.: Morphology for Color Images via Loewner Order for Matrix Fields. In: Mathematical Morphology and Its Applications to Signal and Image Processing (Proc. of ISMM\u201913), LNSC 7883. Springer, pp. 243\u2013254, (2013)","DOI":"10.1007\/978-3-642-38294-9_21"},{"key":"607_CR7","doi-asserted-by":"crossref","unstructured":"van de Gronde, J.J., Roerdink, J.B.T.M.: Group-Invariant Frames for Colour Morphology. In: Mathematical Morphology and Its Applications to Signal and Image Processing (Proc. of ISMM\u201913), LNSC 7883, Springer, pp. 267\u2013278 (2013)","DOI":"10.1007\/978-3-642-38294-9_23"},{"issue":"11","key":"607_CR8","doi-asserted-by":"crossref","first-page":"3301","DOI":"10.1109\/TIP.2011.2144611","volume":"20","author":"S Velasco-Forero","year":"2011","unstructured":"Velasco-Forero, S., Angulo, J.: Supervised ordering in $$\\mathbb{R}^n$$ R n : application to morphological processing of hyperspectral images. IEEE Trans. Image Process. 20(11), 3301\u20133308 (2011)","journal-title":"IEEE Trans. Image Process."},{"issue":"7","key":"607_CR9","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/JSTSP.2012.2211336","volume":"6","author":"S Velasco-Forero","year":"2012","unstructured":"Velasco-Forero, S., Angulo, J.: Random projection depth for multivariate mathematical morphology. IEEE J. Sel. Top. Signal Process. 6(7), 753\u2013763 (2012)","journal-title":"IEEE J. Sel. Top. Signal Process."},{"issue":"3","key":"607_CR10","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.cviu.2006.11.008","volume":"107","author":"J Angulo","year":"2007","unstructured":"Angulo, J.: Morphological colour operators in totally ordered lattices based on distances. Application to image filtering, enhancement and analysis. Comput. Vis. Image Underst. 107(3), 56\u201373 (2007)","journal-title":"Comput. Vis. Image Underst."},{"issue":"1","key":"607_CR11","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jvcir.2009.10.002","volume":"21","author":"J Angulo","year":"2010","unstructured":"Angulo, J.: Geometric algebra colour image representations and derived total orderings for morphological operators Part I: Colour quaternions. J. Visual Commun. Image Represent. 21(1), 33\u201348 (2010)","journal-title":"J. Visual Commun. Image Represent."},{"issue":"2","key":"607_CR12","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.patrec.2007.09.011","volume":"29","author":"E Aptoula","year":"2008","unstructured":"Aptoula, E., Lefevre, S.: On lexicographical ordering in multivariate mathematical morphology. Pattern Recognit. Lett. 29(2), 109\u2013118 (2008)","journal-title":"Pattern Recognit. Lett."},{"key":"607_CR13","doi-asserted-by":"crossref","unstructured":"Hanbury, A.: Mathematical morphology in the HLS colour space. In: Proceedings of the 12th British Machine Vision Conference (BMVC), Manchester, pp. II-451460 (2001)","DOI":"10.5244\/C.15.47"},{"key":"607_CR14","unstructured":"Chanussot, J., Lambert, P.: Total ordering based on space filling curves for multivalued morphology. In: Proceedings of Fourth International Symposium on Mathematical Morphology and its Applications to Image and Signal Processing (ISMM \u201998), pp. 51\u201358, (1998)"},{"key":"607_CR15","unstructured":"Florez-Revuelta, F.: Ordering of the RGB space with a growing self-organizing network. Application to color mathematical morphology. In: Proceedings of the 15th International Conference on Artificial Neural Networks: Biological Inspirations (ICANN\u201905), Part I, pp. 385\u2013390, (2005)"},{"issue":"03","key":"607_CR16","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1142\/S0219467808003192","volume":"8","author":"O Lezoray","year":"2008","unstructured":"Lezoray, O., Meurie, C., Elmoataz, A.: Graph-based ordering scheme for color image filtering. Int. J. Image Graph. 8(03), 473\u2013493 (2008)","journal-title":"Int. J. Image Graph."},{"key":"607_CR17","unstructured":"Ledda, A., Philips, W.: Majority ordering for colour mathematical morphology. In: Proceedings of the XIIIth European Signal Processing Conference, Antalya, Turkey, (2005)"},{"key":"607_CR18","doi-asserted-by":"crossref","unstructured":"Chevallier, E., Angulo, J.: Image adapted total ordering for mathematical morphology on multivariate images. In: Proceedings of IEEE International Conference on Image Processing (ICIP\u201914), (2014)","DOI":"10.1109\/ICIP.2014.7025595"},{"key":"607_CR19","volume-title":"Morphological Image Analysis: Principles and Applications","author":"P Soille","year":"2003","unstructured":"Soille, P.: Morphological Image Analysis: Principles and Applications. Springer, New York (2003)"},{"key":"607_CR20","unstructured":"Chanussot, J.: Approches vectorielles ou marginales pour le traitement d\u2019image multi-composante. Doctoral dissertation (1998)"},{"key":"607_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0871-6","volume-title":"Space Filling Curves","author":"H Sagan","year":"1994","unstructured":"Sagan, H.: Space Filling Curves. Springer, New-York (1994)"},{"key":"607_CR22","doi-asserted-by":"crossref","unstructured":"Rittner, L., de Alencar Lotufo, R.: Segmentation of DTI based on tensorial morphological gradient. In: SPIE Medical Imaging, International Society for Optics and Photonics, pp. 72591E\u201372591E (2009)","DOI":"10.1117\/12.811754"},{"key":"607_CR23","doi-asserted-by":"crossref","unstructured":"van de Gronde, J.J., Roerdink, J.B.T.M.: Sponges for generalized morphology. In: Mathematical Morphology and its Applications to Signal and Image Processing, LNCS, vol. 9082, pp. 351\u2013362. Springer (2015)","DOI":"10.1007\/978-3-319-18720-4_30"},{"key":"607_CR24","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/mrm.20965","volume":"56","author":"V Arsigny","year":"2006","unstructured":"Arsigny, V., Fillard, P., Pennec, X.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Reson. Med. 56, 411\u2013421 (2006)","journal-title":"Magn. Reson. Med."},{"key":"607_CR25","doi-asserted-by":"crossref","unstructured":"Angulo, J., Velasco-Forero, S.: Morphological processing of univariate Gaussian distribution-valued images based on Poincar\u00e9 upper-half plane representation, arXiv:hal-00795012v2 (2013)","DOI":"10.1007\/978-3-319-05317-2_12"},{"issue":"1","key":"607_CR26","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF02096832","volume":"154","author":"GA Gal\u2019perin","year":"1993","unstructured":"Gal\u2019perin, G.A.: A concept of the mass center of a system of material points in the constant curvature spaces. Commun. Math. Phys. 154(1), 63\u201384 (1993)","journal-title":"Commun. Math. Phys."},{"key":"607_CR27","doi-asserted-by":"crossref","unstructured":"Ledoux, A., Richard, A., Capelle-Laiz\u00e9, A.-S.: How to specify or identify the most accurate multispectral distance function for mathematical morphology. In: Colour and Visual Computing Symposium, pp. 1\u20137, (2013)","DOI":"10.1109\/CVCS.2013.6626273"},{"key":"607_CR28","doi-asserted-by":"crossref","unstructured":"Florez-Revuelta, F.: Topology-preserving rdering of the RGB space with an evolutionary algorithm. In: Applications of Evolutionary Computation. Springer International Publishing. pp. 517\u2013528, (2015)","DOI":"10.1007\/978-3-319-16549-3_42"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-015-0607-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-015-0607-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-015-0607-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T08:49:48Z","timestamp":1567327788000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-015-0607-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,5]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["607"],"URL":"https:\/\/doi.org\/10.1007\/s10851-015-0607-7","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,5]]}}}