{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T22:53:16Z","timestamp":1762210396532},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2005,5,1]],"date-time":"2005-05-01T00:00:00Z","timestamp":1114905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2005,5]]},"DOI":"10.1007\/s10851-005-4897-z","type":"journal-article","created":{"date-parts":[[2005,4,14]],"date-time":"2005-04-14T13:05:43Z","timestamp":1113483943000},"page":"333-353","source":"Crossref","is-referenced-by-count":63,"title":["Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems"],"prefix":"10.1007","volume":"22","author":[{"given":"Petros","family":"Maragos","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"1782","DOI":"10.1137\/0151091","volume":"51","author":"G.J.F. Banon","year":"1991","unstructured":"G.J.F. Banon and J. Barrera, ?Minimal representations for translation-invariant set mappings by mathematical Morphology?,SIAM J. Appl. Math., Vol. 51, pp. 1782?1798, 1991.","journal-title":"SIAM J. Appl. Math."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0022-247X(63)90093-3","volume":"6","author":"R. Bellman","year":"1963","unstructured":"R. Bellman and W. Karush, ?On the maximum transform?,J. Math. Anal. Appl., vol. 6, pp. 67?74, 1963.","journal-title":"J. Math. Anal. Appl"},{"key":"CR3","volume-title":"Lattice Theory","author":"G. Birkhoff","year":"1967","unstructured":"G. Birkhoff,Lattice Theory, Amer. Math. Soc.: Providence, Rhode Island, 1967."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/0031-3203(94)00312-A","volume":"9","author":"I. Bloch","year":"1995","unstructured":"I. Bloch and H. Maitre, ?Fuzzy mathematical morphologies: A comparative study?Pattern Recognition 28, Vol. 9, pp. 1341?1387, 1995.","journal-title":"Pattern Recognition 28"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.1109\/83.869190","volume":"9","author":"V. Chatzis","year":"2000","unstructured":"V. Chatzis and I. Pitas, ?A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation?IEEE Trans. Image Process., Vol. 9, pp. 1798?1810, 2000.","journal-title":"IEEE Trans. Image Process."},{"key":"CR6","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/5.21069","volume":"77","author":"G. Cohen","year":"1989","unstructured":"G. Cohen, P. Moller, J.P. Quadrat, and M. Viot, ?Algebraic tools for the performance evaluation of discrete event systems?Proc. IEEE, Vol. 77, pp. 39?58, 1989.","journal-title":"Proc. IEEE"},{"key":"CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-48708-8","volume-title":"Minimax Algebra","author":"R. Cuninghame-Green","year":"1979","unstructured":"R. Cuninghame-Green,Minimax Algebra, Springer-Verlag: New York, 1979."},{"key":"CR8","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1023\/A:1013999431844","volume":"16","author":"T.Q. Deng","year":"2002","unstructured":"T.Q. Deng and H.J.A.M. Heijmans, ?Grey-scale morphology based on fuzzy logic?J. Math. Imaging and Vision, 16, 155?171, 2002.","journal-title":"J. Math. Imaging Vision"},{"key":"CR9","volume-title":"An Introduction to Nonlinear Image Processing","author":"E.R. Dougherty","year":"1994","unstructured":"E.R. Dougherty and J. Astola,An Introduction to Nonlinear Image Processing, SPIE Press: Bellingham, Washington, Vol. TT16, 1994."},{"key":"CR10","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0031-3203(80)90049-7","volume":"12","author":"V. Goetcherian","year":"1980","unstructured":"V. Goetcherian, ?From binary to greytone image processing using fuzzy logic concepts?Pattern Recognition, Vol. 12, pp. 7?15, 1980.","journal-title":"Pattern Recognition"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF00118590","volume":"2","author":"J. Goutsias","year":"1992","unstructured":"J. Goutsias, ?Morphological analysis of discrete random shapes?J. Math. Imaging and Vision, Vol. 2, 193?215, 1992.","journal-title":"J. Math. Imaging Vision"},{"key":"CR12","unstructured":"F. Guichard and J.-M. Morel,Image Analysis and PDEs, Book to appear."},{"key":"CR13","unstructured":"R.M. Haralick and L.G. Shapiro,Computer and Robot Vision, Vol. I, Addison-Wesley, 1992."},{"key":"CR14","first-page":"7","volume":"14","author":"H.J.A.M. Heijmans","year":"1987","unstructured":"H.J.A.M. Heijmans, ?Mathematical Morphology: An algebraic approach?CWI Newsletter, Vol. 14, 7?27, 1987.","journal-title":"CWI Newsletter"},{"key":"CR15","volume-title":"Morphological Image Operators","author":"H.J.A.M. Heijmans","year":"1994","unstructured":"H.J.A.M. Heijmans,Morphological Image Operators, Acad. Press: Boston, 1994."},{"key":"CR16","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0734-189X(90)90148-O","volume":"50","author":"H.J.A.M. Heijmans","year":"1990","unstructured":"H.J.A.M. Heijmans and C. Ronse, ?The algebraic basis of mathematical morphology. Part I: Dilations and erosions?Computer Vision, Graphics, and Image Processing, Vol. 50, pp. 245?295, 1990.","journal-title":"Computer Vision, Graphics, and Image Processing"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1016\/S0893-6080(00)00074-5","volume":"13","author":"V.G. Kaburlasos","year":"2000","unstructured":"V.G. Kaburlasos and V. Petridis, ?Fuzzy lattice neurocomputing (FLN) models?Neural Networks, Vol. 13, pp. 1145?1169, 2000.","journal-title":"Neural Networks"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"33","DOI":"10.3233\/FI-2000-411202","volume":"41","author":"R. Keshet (Kresch)","year":"2000","unstructured":"R. Keshet (Kresch), ?Mathematical morphology on complete semilattices and its applications to image processing?Fundamentae Informatica, Vol. 41, pp. 33?56, 2000.","journal-title":"Fundamentae Informatica"},{"key":"CR19","unstructured":"G.J. Klir and B. Yuan,Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, 1995."},{"issue":"4","key":"CR20","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/1047-3203(92)90043-S","volume":"3","author":"R.P. Loce","year":"1992","unstructured":"R.P. Loce and E.R. Dougherty, ?Optimal morphological restoration: The morphological filter mean-absolute-error theorem?J. Visual Communication & Image Representation, Vol. 3, No. 4, pp. 412?432, 1992.","journal-title":"J. Visual Communication & Image Representation"},{"key":"CR21","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/34.24793","volume":"11","author":"P. Maragos","year":"1989","unstructured":"P. Maragos, ?A representation theory for morphological image and signal processing? IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 11, pp. 586?599, 1989.","journal-title":"IEEE Trans. Pattern Analysis and Machine Intelligence"},{"key":"CR22","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0165-1684(94)90057-4","volume":"38","author":"P. Maragos","year":"1994","unstructured":"P. Maragos, ?Morphological systems: Slope transforms and max?min difference and differential equations?Signal Processing, Vol. 38, pp. 57?77, 1994.","journal-title":"Signal Processing"},{"key":"CR23","unstructured":"P. Maragos, ?Morphological signal and image processing? inThe Digital Signal Processing Handbook, V. Madisetti and D. Williams (Ed.), CRC and IEEE Press, 1998."},{"key":"CR24","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1109\/5.54808","volume":"78","author":"P. Maragos","year":"1990","unstructured":"P. Maragos and R.W. Schafer, ?Morphological systems for multidimensional signal processing?Proc. IEEE, Vol. 78, pp. 690?710, 1990.","journal-title":"Proc. IEEE"},{"key":"CR25","first-page":"61","volume-title":"Mathematical Morphology and Its Application to Image and Signal Processing","author":"P. Maragos","year":"2000","unstructured":"P. Maragos, G. Stamou, and S. Tzafestas, ?A lattice control model of fuzzy dynamical systems in state-space?, inMathematical Morphology and Its Application to Image and Signal Processing, J. Goutsias, L. Vincent and D. Bloomberg (Eds.), Kluwer Acad. Publ.: Boston, 2000, pp. 61?70."},{"key":"CR26","doi-asserted-by":"crossref","unstructured":"P. Maragos and S. Tzafestas, ?Max?Min Control Systems with Applications to Discrete Event Dynamical Systems? inAdvances in Manufacturing: Decision, Control and Information Technology, S.G. Tzafestas (Ed.), Springer-Verlag, 1999, pp. 217?230.","DOI":"10.1007\/978-1-4471-0855-9_21"},{"key":"CR27","unstructured":"P. Maragos, V. Tzouvaras, and G. Stamou, ?Synthesis and applications of lattice image operators based on fuzzy norms?, inProc. Int?l Conf. Image Processing (ICIP-2001), Thessaloniki, Greece, Oct. 2001."},{"key":"CR28","first-page":"412","volume-title":"Proc. Int?l Fuzzy Systems Assoc. World Congress (IFSA-2003)","author":"P. Maragos","year":"2003","unstructured":"P. Maragos, V. Tzouvaras, and G. Stamou, ?Lattice fuzzy image operators and generalized image gradients?, inProc. Int?l Fuzzy Systems Assoc. World Congress (IFSA-2003), Turkey, July 2003. LNCS 2715, Springer-Verlag, 2003, pp. 412?419."},{"key":"CR29","volume-title":"Random Sets and Integral Geometry","author":"G. Matheron","year":"1975","unstructured":"G. Matheron,Random Sets and Integral Geometry, J. Wiley: NY, 1975."},{"key":"CR30","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0165-0114(01)00013-6","volume":"124","author":"M. Nachtegael","year":"2001","unstructured":"M. Nachtegael and E.E. Kerre, ?Connections between binary, gray-scale and fuzzy mathematical morphologies?Fyzzy Sets and Systems, Vol. 124, pp. 73?85, 2001.","journal-title":"Fyzzy Sets and Systems"},{"key":"CR31","first-page":"632","volume":"SMC-8","author":"Y. Nakagawa","year":"1978","unstructured":"Y. Nakagawa and A. Rosenfeld, ?A note on the use of local min and max operations in digital picture processing?IEEE Trans. Syst., Man, Cybern., Vol. SMC-8, pp. 632?635, 1978.","journal-title":"IEEE Trans. Syst., Man, Cybern"},{"key":"CR32","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0743-7315(87)90007-4","volume":"4","author":"G.X. Ritter","year":"1987","unstructured":"G.X. Ritter and P.D. Gader, ?Image algebra techniques for parallel image processing?J. Paral. Distr. Comput., Vol. 4, pp. 7?44, 1987.","journal-title":"J. Paral. Distr. Comput."},{"key":"CR33","unstructured":"G.X. Ritter and J.N. Wilson, ?Image algebra in a nutshell? inProc. 1st ICCV, London, June 1987, pp. 641?645."},{"key":"CR34","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1972","unstructured":"R.T. Rockafellar,Convex Analysis, Princeton Univ. Press: Princeton, 1972."},{"key":"CR35","first-page":"205","volume-title":"Mathematical Morphology in Image Processing","author":"J.B.T.M Roerdink","year":"1993","unstructured":"J.B.T.M Roerdink, ?Mathematical morphology with noncommutative symmetry groups? inMathematical Morphology in Image Processing, E.R. Dougherty (Ed.), Marcel Dekker: NY, 1993, pp. 205?254."},{"key":"CR36","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/1049-9660(91)90076-2","volume":"54","author":"C. Ronse","year":"1991","unstructured":"C. Ronse and H.J.A.M. Heijmans, ?The algebraic basis of mathematical morphology. Part II: Openings and closings?CVGIP: Image Understanding, Vol. 54, pp. 74?97, 1991.","journal-title":"CVGIP: Image Understanding"},{"key":"CR37","volume-title":"Image Analysis and Mathematical Morphology","author":"J. Serra","year":"1982","unstructured":"J. Serra,Image Analysis and Mathematical Morphology, Acad. Press: NY, 1982."},{"key":"CR38","volume-title":"Image Analysis and Mathematical Morphology, Vol. 2, Theoretical Advances","year":"1988","unstructured":"J. Serra (Ed.),Image Analysis and Mathematical Morphology, Vol. 2:Theoretical Advances, Acad. Press: NY 1988."},{"issue":"3","key":"CR39","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/1047-3203(92)90024-N","volume":"3","author":"D. Sinha","year":"1992","unstructured":"D. Sinha and E.R. Dougherty, ?Fuzzy mathematical morphology?J. Visual Communication and Image Representation, Vol. 3, No. 3, pp. 286?302, 1992.","journal-title":"J. Visual Communication and Image Representation"},{"key":"CR40","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0734-189X(86)90004-6","volume":"35","author":"S.R. Sternberg","year":"1986","unstructured":"S.R. Sternberg, ?Grayscale morphology?Comput. Vision, Graph., Image Proc. Vol. 35, pp. 333?355, 1986.","journal-title":"Comput. Vision Graph., Image Proc."},{"key":"CR41","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"L.A. Zadeh","year":"1965","unstructured":"L.A. Zadeh, ?Fuzzy sets?Information and Control, Vol. 8, pp. 338?353, 1965.","journal-title":"Information and Control"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-005-4897-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-005-4897-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-005-4897-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,6]],"date-time":"2020-04-06T21:39:53Z","timestamp":1586209193000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-005-4897-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5]]},"references-count":41,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2005,5]]}},"alternative-id":["4897"],"URL":"https:\/\/doi.org\/10.1007\/s10851-005-4897-z","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5]]}}}