Different averages of a fuzzy set with an application to vessel segmentation

IEEE Transactions on Fuzzy Systems

Volumn 13, Issue 3, 2005, Pages 384-393

  Ayala, Guillermo ^a   León, Teresa ^a   Zapater, Victoria ^a  

^a UNIVERSITY OF VALENCIA   (Spain)

Author keywords

Average fuzzy set; Image segmentation; Mean set; Random set; Retinal vessel detection

Indexed keywords

IMAGE ANALYSIS; IMAGE SEGMENTATION; MATHEMATICAL MODELS; MEDICAL IMAGING; MEMBERSHIP FUNCTIONS; RANDOM PROCESSES;

AVERAGE FUZZY SET; MEAN SET; RANDOM SET; RETINAL VESSEL DETECTION;

FUZZY SETS;

EID: 21444445405     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2004.839667     Document Type: Article

References (28)

1. Z. Arstein and R. A. Vitale, "A strong law of large numbers for random compact sets," Ann. Probab., vol. 3, pp. 879-882. 1975.
2. R. J. Aumann, "Integrals of set-valued functions," J. Math. Anal. Appl., vol. 12, pp. 1-12, 1965.
3. A. J. Baddeley, "Errors in binary images and an V version of the Hausdorff metric," Nieuw Archief Voor Wiskunde, 1992.
4. A. J. Baddeley and I. S. Molchanov, "Averaging of random sets based on their distance functions," J. Math. Imag. Vision, vol. 8, pp. 79-92, 1998.
5. C. Carlsson and R. Fullér, "On possibilistic mean value and variance of fuzzy numbers," Fuzzy Sets Syst., vol. 122, pp. 315-326, 2001.
6. S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, "Detection of blood vessels in retinal images using two-dimensional matched filters," IEEE Trans. Med. Imag., vol. 8. no. 3, pp. 263-269, Sep. 1989.
7. N. A. C. Cressie, Statistics for Spatial Data, revised ed. New York: Wiley, 1993.
8. D. Dubois and H. Prade, "The mean value of a fuzzy number." Fuzzy Sets Syst., vol. 24, pp. 279-300, 1987.
9. Fundamentals of Fuzzy Sets, D. Dubois and H. Prade, Eds.. Kluwer, Norwell, MA, 2000.
10. J. Flynn, "Automatic vessel extraction in digital images," Undergraduate, Electronic Eng. Dept. UCD (dsp.ucd.ie), Dublin, Ireland. 2000.
11. R. Fullér and P. Majlender, "On weighted possibilistic mean and variance of fuzzy numbers," Fuzzy Sets Syst., vol. 135, no. 3, pp. 363-374, 2003.
12. Random Sets Theory and Applications, vol. 97, The IMA Volumes in Mathematics and its Applications, J. Goutsias, R. P. S. Mahler. and H. T. Nguyen, Eds., Springer-Verlag, New York, 1997.
13. C. Heneghan, J. Flynn, M. O'Keefe, and M. Cahill, "Characterization of changes in blood vessel width and tortuosity in retinopathy of prematurity using image analysis," Med. Image Anal., vol. 6, pp. 407-429, 2002.
14. A. Hoover, V. Kouznetsova, and M. Goldbaum, "Locating blood vessels in retinal images by piece-wise threshold probing of a matched filter response," IEEE Trans. Med. Imag., vol. 19, no. 3, pp. 203-210, Mar. 2000.
15. T. Lewis, R. Owens, and A. Baddeley, "Averaging feature maps," Pattern Recogn., vol. 32, pp. 1615-1630, 1999.
16. G. Matheron, Random Sets and Integral Geometry. London, U.K.: Wiley, 1975.
17. N. Otsu, "A threshold selection method from gray-level histograms," IEEE Trans. Syst., Man, Cybern., vol. SMC-9 no. 1, pp. 62-66, Jan. 1979.
18. D. Ralescu, "Average level of a fuzzy set," in Proc. 8th Int. Conf. IPMU Information Processing and Management of Uncertainty in Knowledge-Based Systems, vol. I, Jul. 2000, pp. 190-194.
19. J. Serra, Image Analysis and Mathematical Morphology. New York: Academic, 1982.
20. P. Soille, Morphological Image Analysis. Principles and Applications, 2nd ed. New York: Springer-Verlag, 2003.
21. D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and its Applications, 2nd ed. Berlin, Germany: Wiley, 1995.
22. D. Stoyan and H. Stoyan, Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. New York Wiley, 1994.
23. L. Vincent, Stochastic Geometry Likelihood and Computation. Boca Raton, FL: Chapman Hall/CRC, 1999, vol. 80, Monographs on Statistics and Applied Probability, ch. 6, pp. 199-283.
24. T. Walter, "Application de la morphologie mathématique au diagnostic de la rétinopathie diabétique á partir d' images couleur," Ph.D. dissertation, L' École Nationale Supérieure des Mines de Paris, Paris, France, 2003.
25. F. Zana, "Une approche morphologique pour les detections et bayesienne pour le recalage d'images multimodales: Application aux images retiniennes. Analyze automatique des images angiofluorographiques au cours de la rétinopathie diabétique," Ph.D., Ecole Nationale Supérieure des Mines de Paris, Paris, France, 1999.
26. F. Zana and J. C. Klein, "A multimodal registration algorithm of eye fundus images using vessels detection and Hough transform," IEEE Trans. Med. Imag., vol. 18, no. 5, pp. 419-428, May 1999.
27. F. Zana and J. C. Klein, "Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation," IEEE Trans. Image Process., vol. 10, no. 7, pp. 1010-1019, Jul. 2001.
28. L. Zhou, M. S. Rzeszotarski, L. J. Singerman, and J. M. Chokreff, "The detection and quantification of retinopathy using digital angiograms," IEEE Trans. Med. Imag., vol. 13, no. 10, pp. 619-626, Oct. 1994.