ON A LOSSY IMAGE COMPRESSION/RECONSTRUCTION METHOD BASED ON FUZZY RELATIONAL EQUATIONS

Hirota, Kaoru; Nobuhara, Hajime; Kawamoto, Kazuhiko; Yoshida, Shin-ichi

doi:10.22111/ijfs.2004.492

ON A LOSSY IMAGE COMPRESSION/RECONSTRUCTION METHOD BASED ON FUZZY RELATIONAL EQUATIONS

Document Type : Research Paper

Authors

¹ Kaoru Hirota, Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, 226-8502, Japan

² Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, 226-8502, Japan

10.22111/ijfs.2004.492

Abstract

The pioneer work of image compression/reconstruction based on
fuzzy relational equations (ICF) and the related works are introduced. The
ICF regards an original image as a fuzzy relation by embedding the brightness
level into [0,1]. The compression/reconstruction of ICF correspond to the
composition/solving inverse problem formulated on fuzzy relational equations.
Optimizations of ICF can be consequently deduced based on fuzzy relational
calculus, i.e., computation time reduction/improvement of reconstructed image
quality are correspond to a fast solving method/finding an approximate
solution of fuzzy relational equations, respectively. Through the experiments
using test images extracted from Standard Image DataBAse (SIDBA), the
effectiveness of the ICF and its optimizations are shown.

Keywords

References

[1] A. DiNola, W. Pedrycz, and S. Sessa, Fuzzy Relational Structures: The State-of-Art, Fuzzy
Sets and Systems, Vol. 75, No. 3(1995) 241-262.
[2] A. DiNola, S. Sessa, W. Pedrycz, and E. Sanchez, Fuzzy Relation Equation and Their Applications
to Knowledge Engineering, Kluwer Academic Publishers, 1989.
[3] K. Hirota, and W. Pedrycz, Fuzzy Relational Compression, IEEE Transactions on Systems,
Man, and Cybernetics, Vol. 29 , No. 3(1999) 407-415.
[4] H. Nobuhara, W. Pedrycz, and K. Hirota, Fast Solving Method of Fuzzy Relational Equation
and Its Application to Lossy Image Compression/Reconstruction, IEEE Transactions on
Fuzzy Systems, Vol. 8, No. 3(2000) 325-334.
[5] H. Nobuhara, Y. Takama, and K. Hirota, Image Compression/Reconstruction Based on Various
Types of Fuzzy Relational Equations, The Transaction of The Institute of Electrical
Engineers of Japan (in Japanese), Vol. 121, No. 6 (2001) 1102-1113.
[6] H. Nobuhara, Y. Takama, W. Pedrycz, and K. Hirota, Lossy Image Compression and Reconstruction
Based on Fuzzy Relational Equations,Fuzzy Filters for Image Processing, Springer
(2002) 339-355.
[7] H. Nobuhara, W. Pedrycz, and K. Hirota, A Digital Watermarking Algorithm using Image
Compression Method based on Fuzzy Relational Equation, IEEE International Conference on
Fuzzy Systems, Hawaii, USA, May 12-17 (2002) (CD-Proceedings).
[8] H. Nobuhara, W. Pedrycz, and K. Hirota, Fuzzy Relational Image Compression using Nonuniform
Coders Designed by Overlap Level of Fuzzy Sets, International Conference on Fuzzy
Systems and Knowledge Discovery (FSKD’02), 2002, Singapore (CD-Proceedings).
[9] H. Nobuhara, and K. Hirota, Non-uniform Coders Design for Motion Compression Method by
Fuzzy Relational Equation, International Fuzzy System AssociationWorld Congress, Istanbul,
Turkey, June 29 - July 2, Lecture Notes in Artificiall Intelligence, No. 2715(2003) 428-435.

[10] W. Pedrycz, Fuzzy Relational Equations with Generalized Connectives and Their Applications,
Fuzzy Sets and Systems, Vol. 10 (1983) 185-201.