A NEW FUZZY MORPHOLOGY APPROACH BASED ON THE FUZZY-VALUED GENERALIZED DEMPSTER-SHAFER THEORY

Document Type : Research Paper

Authors

1 RESEARCH ASSISTANT, CONTROL AND INTELLIGENT PROCESSING CENTER OF EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN, P.O. BOX 14395/515, TEHRAN, IRAN.

2 CONTROL AND INTELLIGENT PROCESSING CENTER OF EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN, P.O. BOX 14395/515, TEHRAN, IRAN.

Abstract

In this paper, a new Fuzzy Morphology (FM) based on the Generalized
Dempster-Shafer Theory (GDST) is proposed. At first, in order to clarify the similarity of
definitions between Mathematical Morphology (MM) and Dempster-Shafer Theory (DST),
dilation and erosion morphological operations are studied from a different viewpoint. Then,
based on this similarity, a FM based on the GDST is proposed. Unlike previous FM’s,
proposed FM does not need any threshold to obtain final eroded or dilated set/image. The
dilation and erosion operations are carried out independently but complementarily. The GDST
based FM results in various eroded and dilated images in consecutive α-cuts, making a nested
set of convex images, where each dilated image at a larger α-cut is a subset of the dilated
image at a smaller α-cut. Dual statement applies to eroded images.

Keywords

References

[1] B. N. Araabi, N. Kehtarnavaz and C. Lucas, Restrictions imposed by the fuzzy extension of relations
and functions, Journal of Intelligent and Fuzzy Systems, 11(1/2) (2001) 9-22.
[2] I. Bloch and H. Maitre, Mathematical morphology on fuzzy sets, Proc. Int. Workshop Mathematical
Morphology and its Applications to Signal Processing, Barcelona, Spain, (1993) 151-156.
[3] I. Bloch and H. Maitre, Fuzzy mathematical morphologies: A comparative study, Pattern
Recognition, 28(9) (1995) 1341-1387.
[4] A. P. Dempster, Upper and lower probabilities induced by a multi-valued mapping, Annals of
Mathematical Statistics, 38(2) (1967) 325-339.
[5] C. R. Giardina and D. Sinha, Image processing using pointed fuzzy sets, Proc. VIII SPIE Conf.
Intelligent Robots and Computer Vision: Algorithms and Techniques, Philadelphia, USA, 1192
(1989) 659-668.
[6] V.Goetcherian, From binary to gray tone image processing using fuzzy logic concepts, Pattern
Recognition, 12(1) (1980) 7-15.
[7] R. C. Gonzalez and R. E. Woods, Digital image processing, Prentice Hall, New York, USA, (2002).
[8] M. Kauffman and M. M. Gupta, Fuzzy mathematical models in engineering and management
science, Elsevier, North-Holland, New York, USA (1988).
[9] J. S. J. Lee, R. M. Haralick, and L. G. Shapiro, Morphologic edge detection, IEEE Transactions on
Robotics and Automation, 3(2) (1987) 142-156.
[10] C. Lucas and B. N. Araabi, Generalization of the Dempster-Shafer theory: A fuzzy-valued measure,
IEEE Transactions on Fuzzy Systems, 7(3) (1999) 255-270.
[11] P. Maragos and R. W. Schafer, Morphological filters-Part I: Their set-theoretic analysis and
relations to linear shift-invariant filters, IEEE Transactions on Acoustics, Speech, and Signal
Processing, 35(8) (1987) 1153-1169.
[12] P. Maragos and R. W. Schafer, Morphological filters-Part II: Their relations to median,
order-statistics, and stack filters, IEEE Transactions on Acoustics, Speech, and Signal Processing,
35(8) (1987) 1170-1184.
[13] G. Matheron, Random sets and integral geometry, John Wiley, New York, USA, (1975).
[14] J. Serra, Image analysis and mathematical morphology, Academic press, London, UK, (1982).
[15] J. Serra, Introduction to mathematical morphology, Computer Vision, Graphics and Image
Processing, 35(3) (1986) 283-305.
[16] G. Shafer, A mathematical theory of evidence, Princeton University Press, Princeton, USA, (1976).
[17] D. Sinha and E. R. Dougherty, A General axiomatic theory of intrinsically fuzzy mathematical
morphologies, IEEE Transactions on Fuzzy Systems, 3(4) (1995) 389-403.
[18] D. Sinha and E. R. Dougherty, Fuzzy mathematical morphology, Visual Communication and Image
Representation, 3(3) (1992) 286-302.
[19] D. Sinha, P. Sinha, E. R. Dougherty, and S. Batman, Design and analysis of fuzzy morphological
algorithms for image processing, IEEE Transactions on Fuzzy Systems, 5(4) (1997) 570-584.
[20] R. L. Stevenson and G. R. Arce, Morphological filters: Statistics and further syntactic properties,
IEEE Transactions on Circuits and Systems, 34(11) (1987) 1292-1305.
[21] L. XiangJi and D. RunTao, Fuzzy morphological operators to edge enhancing of images, Proc. 4th
IEEE Int. Conf. Signal Processing, Beijing, China, 2 (1998) 1017-1020.
Iranian Journal of Fuzzy Systems
Volume 1, Issue 2 - Serial Number 2
September and October 2004
Pages 1-14

Files

Share

How to cite

Statistics