Research On Application Of Fractal In Terrain Simulation And Image Compression

Fractal is a powerful tool for describing nature and irregular geometrical figures of nonlinear system. Its application in terrain simulation and image compression has become a hot spot of research recently and has been studied intensively both at home and abroad. Based on deep study of the mainstream algorithms of fractal terrain simulation and several algorithms of fractal image compression, we made improvements of the algorithms. The work of the dissertation is as follows:1. An introduction was made in detail of the basic fractal theory and some representative algorithms of its application in terrain simulation and image compression.2. Considering the disadvantages of conventional triangular midpoint displacement algorithm, i.e., possible cracks, low efficiency of computing and space utilization, we proposed a triangular midpoint displacement algorithm based upon level mapping, which converts recursion into non-recursive iteration of level mapping and eliminates the demerits of conventional algorithm effectively.3. Considering the long encoding time of fractal image compression, we proposed a fast fractal image coding algorithm based on ratio of horizontal and vertical variances. It reduces the number of self-symmetrical transformations from 8 to 4 according to the ratio of horizontal and vertical variances (RHVV) of the image blocks and restricts the codebook blocks to a relatively small sized window for each range block according to its RHVV. Compared with the basic and variance based algorithms, the proposed one can significantly speed up the encoding with a slight degradation of Peak Signal-Noise Ratio (PSNR) and compression ratio.