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.     

Map use: reading,analysis, interpretation

This paper presents a method of combining text and icon label placement in a real-time computing environment. The method computes label configurations based on placement properties, cartographic disturbance, and label overlap. The process is divided into four phases. In the first phase, candidate positions of the text labels are chosen. In the second phase, the same is done for the icon labels. The choice of candidate positions is based on cartographic preference and cartographic disturbance. The removal of overlap between labels is solved, in the third phase, by means of a combinatorial optimization technique (simulated annealing). When there are label pairs in conflict that could not be resolved, the fourth and final step is executed to remove one label in the pair. The success of the proposed method lies in the ability to effectively reduce the search space for the combinatorial optimization. A number of strategies for reducing search space have been evaluated in a case study. The results show that a good search-space-reduction strategy will lead to acceptable solutions for text and icon labeling within a limited processing time.