Umbra-based Improvement of the Probabilistic Box-Counting Fractal Dimension Estimation

Fractal dimension is widely-used for the analysis of signals exhibiting the self-similarity property. For the estimation of the fractal dimension there exist several approaches, the box counting-based approach being the most used. We propose an improvement of the probabilistic box-counting algorithm for the estimation of the fractal dimension, which leads to an increased precision of the estimation. The proposed approach is based on the definition of the umbra of a signal, a concept coming from mathematical morphology. We validate the proposed approach on the Weierstrass function and show experimental results on an EEG signal.