An Evaluation of Fractal Methods for Characterizing Image Complexity

Previously, we developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates three fractal dimension measurement methods that have been implemented in ICAMS: isarithm, variogram, and a modified version of triangular prism. To provide insights into how the fractal methods compare with conventional spatial techniques in measuring landscape complexity, the performance of two spatial autocorrelation methods, Moran's I and Geary's C, is also evaluated. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of surfaces having higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all surfaces, particularly those with high fractal dimensions. As with the fractal techniques, spatial autocorrelation techniques have been found to be useful for measuring complex images, but not images with low dimensionality. Fractal measurement methods, as well as spatial autocorrelation techniques, can be applied directly to unclassified images and could serve as a tool for change detection and data mining.     

The Tenth International Conference and Sixth General Assembly of the International Cartographic Association: A Report

An invertible model is proposed which uses the basis of scale-independence and scale-dependence to capture some of the essential cartographic elements of topographic relief. The model, which uses Fourier and fractal methods in combination with local surface operators, is invertible, and is used to simulate topography. The uses of such simulated topography are discussed, as are the advantages of the particular model used. The model is developed mathematically. and seems in its application to produce terrain with some desirable cartographic traits.