Proceedings PaperMultiscale isotropic morphology and shape approximation using the Voronoi diagram
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The Voronoi diagram of a sample set obtained from a shape boundary can be analyzed to perform morphological erosions, dilations, openings, and closings of the shape with a scaled unit disk as the structuring element. These operations collectively comprise isotropic morphology--meaning the fundamental morphological operations with a parameterized disk operator. The isotropic morphology operations are the basis of multi-scale morphological shape analysis. For instance, features obtained from a series of openings and closings by disks of varying size can be used to characterize a shape over a range of scales. In general, the isotropic morphology operations are a significant class of operations with broad potential applications. The new, Voronoi-diagram-based isotropic morphology algorithm has four significant advantages over existing algorithms: (1) the Voronoi diagram need only be computed once, and then an entire series of scale-based analyses can be performed at low incremental cost; (2) the time/space complexity of the algorithm is independent of the disk radius and depends only on the number of boundary samples; (3) the scale parameter (disk radius) can assume non-integral values; (4) the implied metric is the Euclidean metric, rather than an approximation thereof.