Multiscale isotropic morphology and shape approximation using the Voronoi diagram

Jonathan W. Brandt

doi:10.1117/12.142163

9 April 1993 Multiscale isotropic morphology and shape approximation using the Voronoi diagram

Jonathan W. Brandt

Proceedings Volume 1832, Vision Geometry; (1993) https://doi.org/10.1117/12.142163
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

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.

Citation Download Citation

Jonathan W. Brandt "Multiscale isotropic morphology and shape approximation using the Voronoi diagram", Proc. SPIE 1832, Vision Geometry, (9 April 1993); https://doi.org/10.1117/12.142163

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KEYWORDS

Shape analysis

Vision geometry

Algorithm development

Statistical analysis

Image processing

Visualization

Digital imaging

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