Multi-bands image analysis using local fractal dimension

Aura ConciÉldman de Oliveira Nunes

An important application of fractals is image texture analysis. The main aspect of fractal geometry used in this application is the concept of fractal dimensions to characterize the texture-scaling behavior. A new idea is presented here: the use of fractals of texture identification in multiband image analysis. This is not a simple extension of the usual characterization of multifractal from its local dimension in gray-level images. It is related to examine the interrelationship among the image representation in bands. Moreover, each band can be seen as a set in the 3D space, wich means that its fractal dimension may present results between 2 and 3. Consequently if two bands are considered in one gathering, their structure is a set in the 4D space and its fractal dimension may present results between 2 and 4. For multi-bands image the fractal dimension upper bound can be even larger. In this work, two propositions to handle the multi-band combination are presented. Both defined for whatever combination of bands. As far as we know, no similar approach has been considered until now.

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