OPTICAL DETERMINATION OF FRACTAL DIMENSIONS USING FOURIER-TRANSFORMS

Links between the fractal Hausdorff dimension, the Fourier transform o f two-dimensional scenes, and image segmentation by texture are discus sed. It is shown that the fractal Hausdorff dimension can be derived b y integration of the intensity in the spatial frequency domain (i.e., the Fourier plane) over a set of bandlimited spatial filters. The diff erences between a computational and an optical approach to determine t he Hausdorff dimension are shown, and advantages of each method are di scussed. Possible future directions for research and improvements are mentioned. Simulated fractal scenes are considered as test images for both the computational and the optical approach.