Rough fuzzy set-based image compression

A new coding/decoding scheme based on the properties and operations of rough fuzzy sets is presented. By normalizing pixel values of an image, each pixel value can be interpreted as the degree of belonging of that pixel to the image foreground. The image is then subdivided into blocks which are partitioned and characterized by a pair of approximation sets. Coding uses a codebook, created with a quantization algorithm, to find the best approximating pair for each block, while decoding exploits specific properties of rough fuzzy sets to rebuild the blocks. The method, called by us rough fuzzy vector quantization (RFVQ) relies on the representation capabilities of the vector to be quantized and not on the quantization algorithm, to determine optimal codevectors. A comparison with other fuzzy-based coding/decoding schemes and with DCT and JPEG methods is performed by means of peak signal to noise ratio (PSNR) values. Results show that for low compression rates the proposed method performs well and, in some cases, the PSNR obtained with RFVQ is close to the JPEG's PSNR.