Fractal dimension, only a fraction of the truth?

A sequence of synthetic images is used in order to compare three different fractal dimension estimation methods. The best methods are then applied to TEM images of mouse liver cell nuclei, to see if the methods are able to distinguish between normal cells and cells with induced cancer. The authors find that an ∈-blanket method gives the best estimate of the fractal dimension, and also the best separation between the two types of cells. However, fractal dimension and a simplified lacunarity feature are not sufficient for a reliable discrimination between the two classes of cells. Finally, the authors demonstrate that one can easily derive a fractal dimension related texture feature from the difference in the number of gray level runs at two different gray value quantization widths