Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces

Authors:
H. Nobuhara;K. Hirota;F. Di. Martino;W. Pedrycz;S. Sessa
Affiliations:
Department of Computational Intelligence and System Science, Tokyo Institute of Technology, Midori-ku, Japan 226--8502;Department of Computational Intelligence and System Science, Tokyo Institute of Technology, Midori-ku, Japan 226--8502;Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università degli Studi di Napoli "Federico II", Napoli, Italy 80134;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada T6R 2G7;Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università degli Studi di Napoli "Federico II", Napoli, Italy 80134
Venue:
Fuzzy Optimization and Decision Making
Year:
2005

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Abstract

We use particular fuzzy relation equations for compression/decompression of colour images in the RGB and YUV spaces, by comparing the results of the reconstructed images obtained in both cases. Our tests are made over well known images of 256脳256 pixels (8 bits per pixel in each band) extracted from Corel Gallery. After the decomposition of each image in the three bands of the RGB and YUV colour spaces, the compression is performed using fuzzy relation equations of "min - 驴t" type, where "t" is the Lukasiewicz t-norm and "驴t" is its residuum. Any image is subdivided in blocks and each block is compressed by optimizing a parameter inserted in the Gaussian membership functions of the fuzzy sets, used as coders in the fuzzy equations. The decompression process is realized via a fuzzy relation equation of max-t type. In both RGB and YUV spaces we evaluate and compare the root means square error (RMSE) and the consequentpeak signal to noise ratio (PSNR) on the decompressed images with respect to the original image under several compression rates.