Optical determination of fractal dimensions using Fourier transforms

Reyer Zwiggelaar; Christine R. Bull

doi:10.1117/12.201665

1 May 1995 Optical determination of fractal dimensions using Fourier transforms

Reyer Zwiggelaar, Christine R. Bull

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Optical Engineering, Vol. 34, Issue 5, (May 1995). https://doi.org/10.1117/12.201665

Abstract

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.

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Reyer Zwiggelaar and Christine R. Bull "Optical determination of fractal dimensions using Fourier transforms," Optical Engineering 34(5), (1 May 1995). https://doi.org/10.1117/12.201665

Published: 1 May 1995

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