In this thesis, a higher dimensional extension of the one dimensional Higuchi method wasdeveloped [Higuchi; 1988]. This enables to analyse images and volume data in an easier and moreobjective way. New algorithms were found that show a high accuracy in two and three dimensions.That is especially interesting for medicine, because the measured variable in many cases shows ahigh significance with different pathological grades. The methods were tested for two-dimensionaldata on histological images of cervical intraepithelial neoplasia (CIN). The three-dimensionalalgorithm was tested on MRI volume data of rabbit organs.Due to the fact that the fractal dimensions were measured as the slope of a linear regression, twodifferent ways of optimizing various methods were shown. The first idea is a fit to theoretical valuesof the fractal dimension by adapting the offset and gradient of the linear regression. The second oneis to build a correction that considers the dimension dependency of various methods.Based on the concept of Higuchi, an algorithm was developed to measure the fractal dimension ofRGB images. Further, a method was developed to discriminate between different grades of CINwith an approach that weights the measured dimension with the brightness of the observed data.Moreover, a technique was found to weight the Higuchi dimension with the color spectrum of thecells, which delivers a high significance and therefore, helps to distinguish e.g. between CINgrades.