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

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 256×256 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 - → _t ” type, where “t” is the Lukasiewicz t-norm and “→ _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.