Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions: Image thresholding invariant

Pattern Recognition Letters

Volumn 29, Issue 4, 2008, Pages 525-536

  Bustince, H ^a   Barrenechea, E ^a   Pagola, M ^a  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

Distance measures; Fuzzy entropy; Image thresholding; Implication operators; Restricted dissimilarity functions; Restricted equivalence functions

Indexed keywords

ALGORITHMS; FUNCTION EVALUATION; FUZZY SETS; PATTERN RECOGNITION; THEOREM PROVING;

FUZZY ENTROPY; FUZZY FILTERS; HISTOGRAM ANALYSIS; IMAGE THRESHOLDING; RESTRICTED EQUIVALENCE FUNCTIONS;

IMAGE ANALYSIS;

EID: 38349025356     PISSN: 01678655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patrec.2007.11.007     Document Type: Article

References (54)

1. Baddeley, A.J., 1992. An error metric for images. Robust Computer Vision. Wichmann, Karlsruhe, pp. 59-78.
2. Bandler W., and Kohout L. Fuzzy power sets and fuzzy implication operators. Fuzzy Sets Syst. 4 (1980) 13-30
3. Bezdek J.C., Keller J., Krisnapuram R., and Pal N.R. Fuzzy models and algorithms for pattern recognition and image processing. In: Dubois D., and Prade H. (Eds). The Handbooks of Fuzzy Sets Series, Series (1999), Kluwer Academic Publishers, Boston/London/Dordrecht
4. Borgefors G. Distance transformation in arbitrary dimensions. CVGIP 27 (1984) 321-345
5. Bouchon-Meunier B., Rifqi M., and Bothorel S. Towards general measures of comparison of objects. Fuzzy Sets Syst. 84 (1996) 143-153
6. Brucker F. Sub-dominant theory in numerical taxonomy. Discrete Appl. Math. 154 (2006) 1085-1099
7. Bustince H. Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets. Int. J. Approx. Reason. 23 (2000) 137-209
8. Bustince H., Burillo P., and Soria F. Automorphisms, negations and implication operators. Fuzzy Sets Syst. 134 (2003) 209-229
9. Bustince H., Mohedano V., Barrenechea E., and Pagola M. Definition and construction of fuzzy DI-subsethood measures. Inform. Sci. 176 (2006) 3190-3231
10. Bustince H., Barrenechea E., and Pagola M. Restricted equivalence functions. Fuzzy Sets Syst. 157 (2006) 2333-2346
11. Bustince H., Barrenechea E., and Pagola M. Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets Syst. 158 (2007) 496-516
12. Bustince H., Montero J., Barrenechea E., and Pagola M. Semiautoduality in a restricted family of aggregation operators. Fuzzy Sets Syst. 158 (2007) 1360-1377
13. Calvo T., kolesárová A., Komorníková M., and Mesiar R. Aggregation operators: basic concepts, issues and properties. In: Calvo T., Mayor G., and Mesiar R. (Eds). Studies in Fuzziness and Soft Computing vol. 97 (2002), Springer-Verlag, New York
14. Chaira T., and Ray A.K. Fuzzy measures for color image retrieval. Fuzzy Sets Syst. 150 (2005) 545-560
15. Chaira T., and Ray A.K. Region extraction using fuzzy similarity measures. J. Fuzzy Math. 11 3 (2003) 601-607
16. Chi Z., Yan H., and Pham T. Optimal image thresholding Fuzzy algorithms: with application to image processing and pattern recognition (1998), World Scientific, Singapore (pp. 45-84)
17. Coquin D., and Bolon Ph. Discrete distance operator on rectangular grids. Pattern Recognit. Lett. 16 (1995) 911-923
18. Coquin, D., Bolon, Ph., Chehadeh, Y., 1995. 3D distance operators - application to image comparison. In: Proceedings of the 15th GRETSI Symposium, September 1995, pp. 761-764 (in French).
19. De Luca A., and Termini S. A definition of a nonprobabilistic entropy in the setting of fuzzy set theory. Inform. Contr. 20 (1972) 301-312
20. Diatta J. Description-meet complatible multiway dissimilarities. Discrete Appl. Math. 154 (2006) 493-507
21. Dubois D., and Prade H. A review of fuzzy set aggregation connectives. Inform. Sci. 36 (1985) 85-121
22. Dubois D., Ostasiewicz W., and Prade H. Fuzzy sets: history and basic notions. In: Dubois D., and Prade H. (Eds). Fundamentals of Fuzzy Sets (2000), Kluwer, Boston, MA 21-124
23. Ebanks B. On measures of fuzziness and their representations. J. Math. Anal. Appl. 94 (1983) 24-37
24. Fan J., and Xie W. Some notes on similarity measure and proximity measure. Fuzzy Sets Syst. 101 (1999) 403-412
25. Fan J., Xie X., and Pei J. Subsethood measures: new definitions. Fuzzy Sets Syst. 106 (1999) 201-209
26. Fodor J., and Roubens M. Fuzzy preference modelling and multicriteria decision support. Theory and Decision Library (1994), Kluwer Academic Publishers
27. Forero M.G. Fuzzy thresholding and histogram analysis. In: Nachtegael M., Van der Weken D., Van de Ville D., and Kerre E.E. (Eds). Fuzzy Filters for Image Processing (2003), Springer 129-152
28. Forero, M.G., Rojas, O., 2000. New formulation in image thresholding using fuzzy logic. In: Proceedings of the 11th Portuguese Conference on Pattern Recognition RECPAD2000, pp. 117-124.
29. Forero, M.G., Sierra, E.L., Alvarez, J., Pech, J., Cristobal, G., Alcalá, L., Desco, M., 2001. Automatic sputum color image segmentation for tuberculosis diagnosis. In: Javidi Dahram, V., Psaltis Demetri (Eds.), Proceedings of SPIE: Algorithms and Systems for Optical Information Processing, vol. 4471, pp. 251-261.
30. Glasbey C.A. An analysis of histogram-based thresholding algorithms. CVGIP: Graph. Models Image Process. 55 6 (1993) 532-537
31. Guo L., and Garland M. The use of entropy minimization for the solution of blind source separation problems in image analysis. Pattern Recognit. 39 (2006) 1066-1073
32. Huang L.K., and Wang M.J. Image thresholding by minimizing the measure of fuzziness. Pattern Recognit. 28 1 (1995) 41-51
33. Jan J.S.R., Sun C.T., and Mizutani E. Fuzzy sets. Neuro-Fuzzy Soft Comput. (1997) 13-46
34. Klir G.J., and Folger T.A. Fuzzy Sets Uncertainty and Information (1988), Prentice-Hall International
35. Kolmogoroff A.N. Sur la notion de la moyenne. Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12 (1930) 388-391
36. Lin C.T., and Lee G. Fuzzy measures. Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems (1996), Prentice Hall, Upper Saddle River pp. 63-88
37. Liu X. Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52 (1992) 305-318
38. Nagumo M. Uber eine klasse der mittelwerte. Jpn. J. Math. 6 (1930) 71-79
39. Ovchinnikov S.V., and Roubens M. On strict preference relations. Fuzzy Sets Syst. 43 (1991) 319-326
40. Pal N.R., and Pal S.K. A review of image segmentation techniques. Pattern Recognit. 26 (1993) 1277-1294
41. Pappis C.P., and Karacapilidis N.I. A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Syst. 56 (1993) 171-174
42. Parker J.R. Advanced Method in Grey-level Segmentation, Algorithms for Image Processing and Computer Vision (1997), John Wiley and Sons, New York pp. 116-149
43. Pratt W.K. Image Segmentation Digital Image Processing (1991), John Wiley and Sons, New York pp. 597-627
44. Quang Le S., and Bao Ho T. An association-based dissimilarity measure for categorical data. Pattern Recognit. Lett. 26 (2005) 2549-2557
45. Sahoo P.K., Soltani S., Wong A.K.C., and Chen Y.C. A survey of thresholding techniques. Comput. Vis. Graphics Image Process. 41 (1988) 233-260
46. Sankur B., and Sezgin M. Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13 1 (2004) 146-165
47. Santos Tomás M., Alsina C., and Rubio-Martinez J. Pseudometrics from three-positive semidefinite similarities. Fuzzy Sets Syst. 157 17 (2006) 2347-2355
48. Seaborn M., Hepplewhite L., and Stonham J. Fuzzy colour category map for the measurement of colour similarity and dissimilarity. Pattern Recognit. 38 (2005) 165-177
49. Tizhoosh H.R. Image thresholding using type II fuzzy sets. Pattern Recognit. 38 12 (2005) 2363-2372
50. Trillas, E., 1979. Sobre Funciones de Negación en la Teoría de Conjuntos Difusos. Stochastica, III-1, 47-59 (in Spanish). Reprinted (English version) (1998) In: Barro, S. (Ed.), Advances of Fuzzy Logic. et altri-Universidad de Santiago de Compostela, pp. 31-43.
51. Van der Weken D., Nachtegael M., and Kerre E.E. Using similarity measures and homogeneity for the comparison of images. Image Vis. Comput. 22 (2004) 695-702
52. Wang X., De Baets B., and Kerre E. A comparative study of similarity measures. Fuzzy Sets Syst. 73 (1995) 259-268
53. Yager R.R. On global requirements for implication operators in fuzzy modus ponens. Fuzzy Sets Syst. 106 (1999) 3-10
54. Zadeh L.A. Fuzzy sets. Inform. Contr. 8 (1965) 338-353