A Study On Fractal Theory And Its Application In Image Edge Detection

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. Fractal sets can be iterated to produce complex nature objects and fractal dimension can be used to measure the complexity of objects, so between fractal and image there lies a natural relation, which make it possible to process image based on fractal theory. At present the fractal based applications in image domain are approximately classified into two categories: according to the characteristic of self-similar of fractal, people imitate and compress the natural image using mapping transformation method. This is one category. The other is according to the features of fractal and fractal dimension, people set up image models, investigate the main geometric features of the images and process them effectively. This thesis has studied the fractal theory and its applications in image edge detection. The main works are described as follows:(1) We have summarized the latest research achievements and development of fractal theory and the applications in image processing domain and discussed and studied the definition, principle and algorithm of fractal and fractal dimension;(2) Aiming at the disadvantages of DFBR based edge detection method, an algorithm based on fractal intercept feature was put forward; Moreover, aiming at the bad anti-noise performance of traditional methods, a edge evaluation method was introduced to evaluate the performance of the algorithm and that of Sobel-based algorithm quantificationally;(3) Furthermore, we proposed a novel method based on slope feature and intercept feature, then compared the performance with that of intercept-based method. The experiment results shows that the performance of this algorithm are better than that of intercept-based method;(4) Taking advantages of good anti-noise performance of fractal-based method, we improved the traditional methods and proposed a algorithm which combined the traditional method with fractal theory achieved a better anti-noise performance.