Image Compression Based on Mapping Image Fractals to Rational Numbers

Abstract

The advent of the Internet era and advances in telecommunications has seen image compression attract a great deal of research. Enhancements to the quality and ratio of image compression have been achieved through approaches, such as neural networks and discrete transforms. However, other heuristic and bio-inspired methods, such as genetic algorithms, are still in the developmental stages. In this paper, we introduce a new image compression mechanism that exploits the relationship between rational numbers and their corresponding quotient representation. Each sub-image is mapped to a fractional number based on its RGB representation, and this fraction is then reduced to an efficient quotient. The appeal of using genetic algorithms is explained by the massive search needed to find a close fraction that can be reduced to a short quotient. We enhance the search by pre-calculating all possible rational numbers for a given set of numerators and denominators. Experimental results show that a considerable compression ratio can be achieved when the least significant bits of each byte are altered. Hence, the image quality is preserved while achieving a high compression ratio.

Keywords

• Fractal image
• lossy compression
• rational numbers
• genetic algorithms
• Mersenne numbers