One important applications of fractals is the field of image texture analysis. The main aspect of fractal geometry used in such application is the concept of fractal dimensions to characterize the texture scaling behavior. However, this identification with fractal makes sense only within certain limits. Moreover sets with the same fractal dimension may differ substantially in their structure. One proposition to handle this is to describe the set not only by one fractal dimension, but by a set of dimensions with their properties. We propose the characterization of multifractal set by the local Hausdorff dimension and two local box-counting dimensions. A new idea for Hausdorff dimension calculation of images is also presented.
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