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Homogeneous fractals and their application in texture analysis

: Müssigmann, U.

Peitgen, H.-O.; Henriques, J.M.; Penedo, L.F.:
Fractal '90. 1st IFIP Conference on Fractals
Amsterdam: North-Holland Publishing, 1991
ISBN: 0-444-88757-1
Fractals in the Fundamental and Applied Sciences <1, 1990, Lisbon>
Fraunhofer IPA ()
Bildverarbeitung; fractal dimension; Fraktal; fraktale Dimension; Hausdorff dimension; image analysis; Minkowski dimension; Scale Space Filtering; Texturanalyse; texture analysis

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.