Fractal Case Study for Mammary Cancer: Analysis of Interobserver Variability

This paper discusses some features of the distribution of box-counting fractal dimension measured on a real data set from mammary cancer and masthopathy patients. During the study we found several reasons why mammary cancer and its following distribution cannot be easily represented by single box-counting dimension. The main problem is that without a histopathological examination of the tumor a simple algorithm based only on single box-counting dimension is difficult to be constructed. We have tried to understand the distribution underlying the real data, especially its departures from normality. Both normal and gamma distributions are related to the Tweedy distributions, which are given by multi-fractal dimension spectra present in histopathological images. Without having a histological examination of the data multifractality is unavoidable as can be seen from several analysis in this paper. We have seen a fair differentiation between the cancer and masthopathy. Finally we studied the depths of the data based on the information divergence. Some practical conclusions are also given.