Image Pyramids as a New Approach for the Determination of Fractal Dimensions

Abstract

The consideration of different scales and the application of fractal methods on digital images is of high importance if real world objects are investigated. In this context the fractal dimension is an important parameter to characterize structures and patterns. An accurate understanding of them is obligatory if significant and comparable results should be obtained. Recently a new method using an image pyramid approach was compared to the very popular Box Counting Method. The intriguing results showed that a trustable value for the fractal dimension could be obtained in much faster computational times compared to traditional Box Counting algorithms. In addition to these results of this new approach, which is only applicable to binary (black/white) images, we present developments toward the application to grey value/color images. Especially the determination of the grey value surface and the interpolation used to downscale the images seem to have major influence on the results achieved.