FRACTAL DIMENSION AND LACUNARITY ESTIMATED BY SEQUENTIAL 1D POLYGONIZATION OF 2D IMAGES

A new method for estimating fractal dimension is introduced, based on polygonization of 1D curves obtained by scanning 2D images. A strategy for automatic determination of the range of scales where the image is approximately fractal is described. Two new lacunarity measures are also introduced. The method has been compared to several different methods for estimation of fractal dimension and lacunarity. The test set contains a sequence of synthetic images with known fractal parameters, as well as digitized TEM images of mouse liver cell nuclei. The method seems well suited for segmentation purposes.