Lacunarity as a novel measure of cancer cells behavior

An important goal in many branches of science, especially in molecular biology and medicine is the quantitative analysis of the structures and their morphology. The morphology can be analyzed in many ways, in particular by the fractal analysis. Apart from the fractal dimension, an important part of the fractal analysis is the lacunarity measurement which, roughly speaking, characterizes the distribution of gaps in the fractal: a fractal with high lacunarity has large gaps. In this paper, we present an extension of the lacunarity measure to objects with nonregular shapes that enables us to provide a successful discrimination of cancer cell lines. The cell lines differ in the shape of vacuole (the gaps in their body) which is perfectly suited for the lacunarity analysis.