Multifractal Framework Based on Blanket Method

Abstract

This paper proposes two local multifractal measures motivated by blanket method for calculation of fractal dimension. They cover both fractal approaches familiar in image processing. The first two measures (proposed Methods 1 and 3) support model of image with embedded dimension three, while the other supports model of image embedded in space of dimension three (proposed Method 2). While the classical blanket method provides only one value for an image (fractal dimension) multifractal spectrum obtained by any of the proposed measures gives a whole range of dimensional values. This means that proposed multifractal blanket model generalizes classical (monofractal) blanket method and other versions of this monofractal approach implemented locally. Proposed measures are validated on Brodatz image database through texture classification. All proposed methods give similar classification results, while average computation time of Method 3 is substantially longer.