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JACIII Vol.8 No.4 pp. 373-378
doi: 10.20965/jaciii.2004.p0373
(2004)

Paper:

A Fuzzification of Morphological Wavelets Based on Fuzzy Relational Calculus and its Application to Image Compression/Reconstruction

Hajime Nobuhara, and Kaoru Hirota

Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan

Received:
September 25, 2003
Accepted:
March 29, 2004
Published:
July 20, 2004
Keywords:
fuzzy relation, ordered structure, image compression/reconstruction, morphological wavelets
Abstract

A new style of fuzzy wavelets is proposed by the fuzzification of morphological wavelets. Due to the correspondence of the morphological wavelets operations and fuzzy relational ones, wavelets analysis/synthesis schemes can be formulated based on fuzzy relational calculus. To enable efficient image compression/reconstruction, the concept of the alpha-band which is an alpha-cut generalization, is also proposed for thresholding wavelets. In an image compression/reconstruction experiment using test images extracted from the Standard Image DataBAse (SIDBA), it is confirmed that the root mean square error (RMSE) of the proposed soft thresholding is decreased to 87.3% of conventional hard thresholding, when the original image is “Lenna.”

Cite this article as:
Hajime Nobuhara and Kaoru Hirota, “A Fuzzification of Morphological Wavelets Based on Fuzzy Relational Calculus and its Application to Image Compression/Reconstruction,” J. Adv. Comput. Intell. Intell. Inform., Vol.8, No.4, pp. 373-378, 2004.
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