On the Application of Invariant Image Parameters to Fractal Encoding of Bi-Level Images

Article type: Research Article

Authors: Valantinas, Jonas | Žumbakis, Tomas

Affiliations: Department of Applied Mathematics, Kaunas University of Technology, Studentų 50, LT-51368 Kaunas, Lithuania, e-mail: jonas.valantinas@ktu.lt

Abstract: Fractal image compression is an engaging and worthwhile technology that may be successfully applied to still image coding, especially at high compression ratios. Unfortunately, the large amount of computation needed for the image compression (encoding) stage is a major obstacle that needs to be overcome. In spite of numerous and many-sided attempts to accelerate fractal image compression times, the “speed problem” is far from being carried to its conclusion. In the paper, a new version (strategy) of the fractal image encoding technique, adapted to process bi-level (black and white) images, is presented. The strategy employs the necessary image similarity condition based on the use of invariant image parameters (image smoothness indices, image coloration ratios, etc.). It is shown that no images can be similar (in the mean squared error sense) if their respective parameter values differ more than somewhat. In the strategy proposed, the necessary image similarity condition plays a key role – it is applied to speed-up the search process for optimal pairings (range block-domain block), i.e., it enables to narrow the domain pool (search region) for each range block. Experimental analysis results show that implementation of the new fractal image encoding strategy accelerates bi-level image compression times considerably. Exceptionally good results (compression times and quality of restored images) are obtained for silhouette images.

Keywords: digital images, invariant image parameters, fractal image compression

Journal: Informatica, vol. 18, no. 3, pp. 463-478, 2007