## Publica

Hier finden Sie wissenschaftliche Publikationen aus den Fraunhofer-Instituten. # Homogeneous fractals and their application in texture analysis

**Abstract**

The theory of multi-fractals can be used for a complete physical characterization of a fractal set which is inhomogeneous in some sense. The aim of this paper is to prove some basic properties of multi-fractal sets which is done by introducing the local Hausdorff dimension and the local Minkowski dimension. With these definitions of local fractal dimensions we are able to calculate a partition of a fractal set into subsets which are homogeneous with respect to the fractal dimension. For the numerical computation of the fractal dimension we use the so-called scale space filtering which has been used in image analysis to describe a discrete signal by its extrema.