On the role of complete lattices in mathematical morphology: From tool to uncertainty model

Information Sciences

Volumn 181, Issue 10, 2011, Pages 1971-1988

  Nachtegael, M ^a   Sussner, P ^b   Melange T ^a   Kerre, E E ^a  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Complete lattice; Interval valued fuzzy set; Intuitionistic fuzzy set; Mathematical morphology; Modeling uncertainty in image processing

Indexed keywords

COMPLETE LATTICES; FUZZY INTERVAL; FUZZY MATHEMATICAL MORPHOLOGY; GRAY SCALE; GRAY-SCALE IMAGES; GRAYSCALE MORPHOLOGY; IMAGE CAPTURES; INTERVAL-VALUED FUZZY SETS; INTUITIONISTIC FUZZY SETS; MODELING UNCERTAINTY IN IMAGE PROCESSING; MORPHOLOGICAL MODEL; SPATIAL POSITIONS; THRESHOLD APPROACH; UNCERTAINTY MODELS;

FUZZY LOGIC; FUZZY SETS; IMAGE PROCESSING; IMAGING SYSTEMS; MATHEMATICAL MORPHOLOGY; MORPHOLOGY;

FUZZY SET THEORY;

EID: 77958516150     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.03.009     Document Type: Article

References (44)

1. K. Atanassov, Intuitionistic Fuzzy Sets, Technical Report, Bulgarian Academy of Science, Central Technical Library, 1983.
2. K. Atanassov Intuitionistic Fuzzy Sets 1999 Physica Verlag Heidelberg, Germany
3. E. Barrenechea, Image Processing with Interval-valued Fuzzy Sets - Edge Detection - Contrast, Ph.D. Thesis, Public University of Navarra, 2005.
4. I. Bloch, Mathematical morphology on bipolar fuzzy sets, in: Proceedings of ISMM 2007 (International Symposium on Mathematical Morphology), 2007, pp. 3-4.
5. I. Bloch, Dilation and erosion of spatial bipolar fuzzy sets, in: Lecture Notes in Artif (Pubitemid 350270304)
6. I. Bloch, H. Heijmans, and C. Ronse Mathematical morphology M. Aiello, I. Pratt-Hartmann, J. van Benthem, Handbook of Spatial Logics 2007 Springer 857 944
7. A.E. Brito, and O. Kosheleva Interval + image = wavelet: for image processing under interval uncertainty, wavelets are optimal Reliable Computing 4 3 1998 291 301 (Pubitemid 128517406)
8. S.D. Cabrera, K. Iyer, G. Xiang, V. Kreinovich, On inverse halftoning: computational complexity and interval computations, in: Proceedings of CISS 2005 (39th Conference on Information Sciences and Systems), The John Hopkins University, paper 164, 2005.
9. O. Castillo, and P. Melin Intelligent systems with interval type-2 fuzzy logic International Journal of Innovative Computing, Information and Control 4 4 2008 771 783
10. C. Cornelis, G. Deschrijver, and E.E. Kerre Implication in intuitionistic and interval-valued fuzzy set theory: construction, classification, application International Journal of Approximate Reasoning 35 2004 55 95
11. B. De Baets Fuzzy morphology: a logical approach B.M. Ayyub, M.M. Gupta, Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach 1997 Kluwer Academic Publishers Boston 53 67
12. T.Q. Deng, and H.J.A.M. Heijmans Grey-scale morphology based on fuzzy logic Journal of Mathematical Imaging and Vision 16 2 2002 155 171 (Pubitemid 34239176)
13. G. Deschrijver, and E.E. Kerre On the relationship between some extensions of fuzzy set theory Fuzzy Sets and Systems 133 2003 227 235
14. G. Deschrijver, C. Cornelis, and E.E. Kerre On the representation of intuitionistic fuzzy t-norms and t-conorms IEEE Transactions on Fuzzy Systems 12 1 2004 45 61
15. G. Deschrijver, and C. Cornelis Representability in interval-valued fuzzy set theory International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15 3 2007 345 361 (Pubitemid 46978269)
16. D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, and H. Prade Terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets Fuzzy Sets and Systems 156 3 2005 485 491 (Pubitemid 41475504)
17. J. Goguen L-fuzzy sets Journal of Mathematical Analysis and Applications 18 1967 145 174
18. P. Hajek Metamathematics of Fuzzy Logic 1998 Kluwer Academic Publishers Dordrecht
19. R.M. Haralick, S.R. Sternberg, and X. Zhuang Image analysis using mathematical morphology IEEE Transactions on Pattern Analysis and Machine Intelligence 9 4 1987 532 550 (Pubitemid 17632080)
20. 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 50 1990 245 295 (Pubitemid 20695762)
21. H. Heijmans Morphological Image Operators 1994 Academic Press New York, NY
22. J.M. Mendel Computing with words: Zadeh, Turing, Popper and Occam IEEE Computational Intelligence Magazine 2 4 2007 10 17
23. J. Montero, D. Gomez, and H. Bustince On the relevance of some families of fuzzy sets Fuzzy Sets and Systems 158 22 2007 2429 2442 (Pubitemid 47374796)
24. M. Nachtegael, and E.E. Kerre Connections between binary, grayscale and fuzzy mathematical morphologies Fuzzy Sets and Systems 124 1 2001 73 86
25. M. Nachtegael, and E.E. Kerre Decomposing and constructing of fuzzy morphological operations over alpha-cuts: continuous and discrete case IEEE Transactions on Fuzzy Systems 8 5 2000 615 626
26. M. Nachtegael, and E.E. Kerre Fuzzy mathematical morphology: state of the art E.E. Kerre, M. Nachtegael, Fuzzy Techniques in Image Processing Studies in Fuzziness and Soft Computing vol. 52 2000 Springer Verlag Heidelberg 3 57
27. M. Nachtegael, H. Heijmans, D. Van der Weken, E.E. Kerre, Fuzzy adjunctions in mathematical morphology, in: Proceedings of JCIS 2003 (Seventh Joint Conference on Information Sciences), 2003, pp. 202-205.
28. M. Nachtegael, P. Sussner, T. Mélange, E.E. Kerre, Some aspects of interval-valued and intuitionistic fuzzy mathematical morphology, in: Proceedings of IPCV 2008 - International Conference on Image Processing, Computer Vision and Pattern Recognition, 2008, pp. 538-543.
29. M. Nachtegael, P. Sussner, T. Mélange, E.E. Kerre, An interval-valued fuzzy morphological model based on Lukasiewicz-operators, in: Lecture Notes in Computer Science (Advanced Concepts for Intelligent Vision Systems - Proceedings of ACIVS 2008), vol. 5259, 2008, pp. 601-612.
30. C. Ronse Why mathematical morphology needs complete lattices Signal Processing 21 2 1990 129 154
31. C. Ronse Flat morphology on power lattices Journal of Mathematical Imaging and Vision 26 1-2 2006 185 216 (Pubitemid 44832628)
32. S. Schulte, M. Nachtegael, V. De Witte, D. Van der Weken, E.E. Kerre, Fuzzy impulse noise reduction methods for color images, in: Proceedings of Fuzzy Days 2006 (International Conference on Computational Intelligence), Dortmund, Germany, pp. 711-720.
33. S. Schulte, V. De Witte, M. Nachtegael, T. Mélange, E.E. Kerre, A new fuzzy additive noise reduction method, in: Lecture Notes in Computer Science (Image Analysis and Recognition - Proceedings of ICIAR 2007), vol. 4633, 2007, pp. 12-23, ISBN: 978-3-540-74258-6.
34. J. Serra Image Analysis and Mathematical Morphology 1982 Academic Press London
35. J. Serra Image Analysis and Mathematical Morphology II: Theoretical Advances 1988 Academic Press London
36. P. Smets, and P. Magrez Implication in fuzzy logic International Journal of Approximate Reasoning 1 1987 327 347
37. P. Sussner, and M.E. Valle Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality Journal of Mathematical Imaging and Vision 32 2 2008 139 159
38. P. Sussner, M. Nachtegael, T. Mélange, L-fuzzy mathematical morphology: an extension of interval-valued and intuitionistic fuzzy mathematical morphology, in: Proceedings of NAFIPS 2009 - 28th North American Fuzzy Information Processing Society Annual Conference, 2009, 6 pages on CD.
39. I.B. Turksen, and Z. Zhong An approximate analogical reasoning schema based on similarity measures and interval-valued fuzzy sets Fuzzy Sets and Systems 34 3 1990 323 346
40. E. Vansteenkiste, D. Van der Weken, W. Philips, and E.E. Kerre Evaluation of the perceptual performance of fuzzy image quality measures Lecture Notes in Computer Science 4251 2006 623 630 (Pubitemid 44700149)
41. I.K. Vlachos, D.G. Sergiadis, Towards intuitionistic fuzzy image processing, in: Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, 2005, pp. 2-7.
42. I.K. Vlachos, and D.G. Sergiadis Intuitionistic fuzzy information - applications to pattern recognition Pattern Recognition Letters 28 2006 197 206
43. I.K. Vlachos, D.G. Sergiadis, Hesitancy histogram equalization, in: Proceedings of FUZZ-IEEE 2007, 2007, pp. 1-6.
44. L. Zadeh Fuzzy sets Information Control 8 1965 338 353