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Implementation and comparison of fractal dimension estimative methods and their use on analysis and image processing.

André Ricardo Backes

Instituto de Ciências Matemáticas e de Computação - Universidade de São Paulo, 2006

Fractal Dimension can be used to measure some characteristics related to the image complexity, allowing its use on shape and texture analysis and pattern recognition. In this work is presented a comparative study among some of the most important methods to estimate Fractal Dimension. It was performed a experimental analysis and a case study for each one of the techniques, considering implementation aspects, precision, variation of results under parameters adjustments and noise tolerance. In this work is also performed a study about MultiScale Fractal Dimension, aiming at its use as a methodology of complexity signature. In the literature the multiscale technique is limited to Bouligand-Minkowski method, being here it extended to other methodologies of estimative of Fractal Dimension. By experimental analysis the proposed methodologies were compared and the results argued, emphasizing the advantages and disadvantages of those techniques.

keywords: Boxcounting,Complexity,Fractal dimension,Lacunarity,Minkowski,Multi-scale fractal dimension,Shape analysis,Texture