Fractal Dimension of Color Fractal Images

Fractal dimension is a very useful metric for the analysis of the images with self-similar content, such as textures. For its computation there exist several approaches, the probabilistic algorithm being accepted as the most elegant approach. However, all the existing methods are defined for 1-D signals or binary images, with extension to grayscale images. Our purpose is to propose a color version of the probabilistic algorithm for the computation of the fractal dimension. To validate this new approach, we also propose an extension of the existing algorithm for the generation of probabilistic fractals, in order to obtain color fractal images. Then we show the results of our experiments and conclude this paper.

[1]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..

[2]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[3]  R. Voss.  Characterization and Measurement of Random Fractals , 1986 .

[4]  James M. Keller,et al.  Texture description and segmentation through fractal geometry , 1989, Comput. Vis. Graph. Image Process..

[5]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[6]  R. Voss.  Random Fractals: characterization and measurement , 1991 .

[7]  C. Allain,et al.  Characterizing the lacunarity of random and deterministic fractal sets. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[8]  Petros Maragos,et al.  Energy separation in signal modulations with application to speech analysis , 1993, IEEE Trans. Signal Process..

[9]  Petros Maragos,et al.  Measuring the Fractal Dimension of Signals: Morphological Covers and Iterative Optimization , 1993, IEEE Trans. Signal Process..

[10]  Nirupam Sarkar,et al.  An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[11]  Qian Huang,et al.  Can the fractal dimension of images be measured? , 1994, Pattern Recognit..

[12]  Bidyut Baran Chaudhuri,et al.  Texture Segmentation Using Fractal Dimension , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  W. Hargrove,et al.  Lacunarity analysis: A general technique for the analysis of spatial patterns. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  S. Baronti,et al.  Robust estimation of image fractal dimension based on pyramidal decomposition , 1999, ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357).

[15]  Eiichi Honda,et al.  Correlation of Measured Fractal dimensions with lacunarities in computer-Generated Threee-Dimensional Images of Cantor Sets and Those of Fractional Brownian Motion , 1999 .

[16]  Oscar Castillo,et al.  A new method for fuzzy estimation of the fractal dimension and its applications to time series analysis and pattern recognition , 2000, PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500).

[17]  Chih-Ming Hsieh,et al.  Algorithms to estimating fractal dimension of textured images , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[18]  Christine Fernandez-Maloigne,et al.  Content-based image retrieval and high-level representations , 2001, IS&T/SPIE Electronic Imaging.

[19]  Nikos Papamarkos,et al.  Color image retrieval using a fractal signature extraction technique , 2002 .

[20]  Andrzej Bargiela,et al.  Fuzzy fractal dimensions and fuzzy modeling , 2003, Inf. Sci..

[21]  Yung-Chang Chen,et al.  Ultrasonic Liver Tissues Classification by Fractal Feature Vector Based on M-band Wavelet Transform , 2001, IEEE Trans. Medical Imaging.

[22]  K. O. Niemann,et al.  Simulation and quantification of the fine-scale spatial pattern and heterogeneity of forest canopy structure: A lacunarity-based method designed for analysis of continuous canopy heights , 2005 .

[23]  Aglaia G. Manousaki,et al.  Use of color texture in determining the nature of melanocytic skin lesions - a qualitative and quantitative approach , 2006, Comput. Biol. Medicine.

[24]  Shunlin Liang,et al.  Fractal analysis of remotely sensed images: A review of methods and applications , 2006 .

[25]  Stefan Jansson.  Evaluation of methods for estimating fractal properties of intensity images , 2006 .

[26]  Witold Kinsner,et al.  A unified approach to fractal dimensions , 2005, Fourth IEEE Conference on Cognitive Informatics, 2005. (ICCI 2005)..

[27]  Richard P. Taylor,et al.  The Visual Complexity of Pollock’s Dripped Fractals , 2008 .