Optical Determination of Fractal Dimensions Using Fourier Transforms

Links between the fractal Hausdorff dimension, the Fourier transform of two-dimensional scenes, and image segmentation by texture are discussed. It is shown that the fractal Hausdorff dimension can be derived by integration of the intensity in the spatial frequency domain (i.e., the Fourier plane) over a set of bandlimited spatial filters. The differences between a computational and an optical approach to determine the Hausdorff dimension are shown, and advantages of each method are discussed. 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