论文信息 - Fractal analysis and multifractal spectra for the images

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.

Artde D. K. T. Lam | Q. Li

[1] B. Mandelbrot. Fractal Geometry of Nature , 1984 .

[2] Arnaud E. Jacquin,et al. Image coding based on a fractal theory of iterated contractive image transformations , 1992, IEEE Trans. Image Process..

[3] H. Stanley,et al. Multifractal phenomena in physics and chemistry , 1988, Nature.

[4] Manuel Contero,et al. Textile and tile pattern design automatic cataloguing using detection of the plane symmetry group , 2003, Proceedings Computer Graphics International 2003.

[5] José Miguel Valiente,et al. Structural description of textile and tile pattern designs using image processing , 2004, ICPR 2004.

[6] W. Jeżewski. Complex multifractal measures and a generalized multifractal formalism , 2001 .

[7] Shyi-Long Lee,et al. Multifractal analysis of growing surfaces , 2004 .

[8] J. Peyriére. Multifractal formalisms: Boxed versus centered intervals , 2003 .

[9] B. Mandelbrot,et al. Fractal character of fracture surfaces of metals , 1984, Nature.

[10] K. Stefański. Fractals: form, chance and dimension : B.B. Mandelbrot (International Business Machines, Thomas J. Watson Research Center) : W.H. Freeman and Co., San Francisco, 1977, XVI + 365 pp. , 1985 .

[11] Christopher Frauenberger,et al. Mode independent interaction pattern design , 2005, Ninth International Conference on Information Visualisation (IV'05).