The Research Of Image Compression And Edge Detection Based On The Fractal Theory

Fractal and fractal geometry provide a more exact mathematical model to describe the external world, which broke though the situation limited to Euclid geometry and have drawn much attention from chemists, mathematicians, physicists in various disciplines. At present the fractal based applications in image domain are approximately classified into two categories: compressing image using Iterated Function System and anlysising and processing image effectively according to the fractal dimension. This thesis studies the fractal theory at first, and then, studies the image compression and image edge detection based on the fractal theory.The fractal image encoding based on tiles' partition which was proposed by Jacquin is the base of fast fractal image encoding. This thesis studies this basic method at first, which needs much computation and. coding time; and then studies the fractal image encoding based on mean square value, which needs less computation and the encoding time, has higher compression ratio while the decoding image has hardly been degraded.Image edge detection is one of the classic techniques in image processing. After the study of the classic image edge detection, this thesis studies the image edge detection based on the fractal theory. The method based on the self-similar proves the possibility of detecting the image edge; the image edge detection based on IFS is more complex, but the result is better; the image edge detection based on the DFBR field is fit for the images which has better characteristics of self-similar and radom distribution.