Translation and rotation invariant method of Renyi dimension estimation. (September 2018) - Dlask, Martin; Kukal, Jaromir
Highlights: novel method of correlation dimension estimation based on Parzen estimate modified Renyi entropy as a translational and rotation invariant measure theoretically and numerically proven relationship to correlation dimension efficiency proved on the fractal sets with known dimension Abstract: A fractal dimension is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented, and for the analysis of correlation dimension, a novel approach that employs the log-linear dependence of a modified Renyi entropy is used. The new formula for the Renyi entropy has been investigated both theoretically and experimentally on selected fractal sets.