Fractal analysis and multifractal spectra for the images

The surface shape and microstructure of images, especially digital images, have important influence to construct such characteristics as analysis, transformation and compression to the images, etc. The main purpose of this paper is to use the fractal dimension and multifractal spectra to analyze the characteristics of the images. We will first give a brief description of Fractal Theory and then, the characteristic analysis of the images. Based on box-counting method, an algorithm is derived to calculate the fractal dimension and multifractal spectra of images. Then, a computing program of the fractal dimension and multifractal spectra is developed with help of MATLAB. Through this program, the surface shape and microstructure of images are described. The results of this thesis developed an effective tool to analysis the surface characteristics of images.