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Open Access Publications from the University of California

The Comparison of Complexity Measures for Cartographic Lines (90-1)


The concept of ’line complexity’ is often used in cartography in relation to geometric shape of linear features. The concept is particularly important in automated line generalization. Many measures have been applied over the years in an attempt to describe the shape of irregular one-dimensional features in a quantifiable manner. All of them are narrowly focused on single characteristics of complexity, and moreover they remain in an unknown relationship to one another. This project reviews methods and techniques of capturing the complexity of lines. Further, it explores the existing relationships between eight measures of geometric shape of lines. The measures selected for the analysis involve such characteristics of shape as density of detail, length, angularity, and fractal dimension. The analysis performed on an especially designed test data set, comprising of both natural and cultural features, involves principal components analysis. The recommendations for future research on the topic are presented.

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