Pebble_Pond: a morphological wave propagation algorithm for representing spatial point patterns

Michael M. Skolnick; Peter Marineau

doi:10.1117/12.60654

1 June 1992 Pebble_Pond: a morphological wave propagation algorithm for representing spatial point patterns

Michael M. Skolnick, Peter Marineau

Proceedings Volume 1769, Image Algebra and Morphological Image Processing III; (1992) https://doi.org/10.1117/12.60654
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

Pebble_Pond performs morphologically-based wave propagation on an input set of points on the plane, with the points corresponding to the locations of detected image features. The waves are allowed to pass through each other, resulting in an complex evolving state space from which can be obtained a diverse class of non-planar spatial measures and structures, e.g., all k nearest neighbors, k-th order Voronoi tessellations, and k-th order Gabriel graphs. One perspective on Pebble_Pond is that it takes spatial structure and transforms it into temporal structure. That is, at each iteration in the wave propagation, measures on the state space reflect spatial structure at the scale corresponding to the current iteration. Thus, at each iteration all measures obtained (in parallel) from the state space report on all spatial relations falling within the distance that the waves have propagated. This paper investigates particular measures of the underlying state space that provide a rotation and scale invariant signature of the spatial relationship between planar points. Also, based on preliminary data, the signature is robust with respect to spurious points, i.e., spatial commonalities are preserved amongst the differences. The measures are based upon the formation of an evolving grey-scale surface which corresponds to the cardinality of the intersection of the point wave sources. The centroids of the local maxima of these intersection surfaces are used as normalizing origins from which to plot the relative angles of nearby wave front crossings. The signature plots the relative angles of wave crossings (with respect to their local maxima centroids) that evolve over time as local maxima regions arise and combine to form new local maxima regions.

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Michael M. Skolnick and Peter Marineau "Pebble_Pond: a morphological wave propagation algorithm for representing spatial point patterns", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); https://doi.org/10.1117/12.60654

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KEYWORDS

Wave propagation

Wavefronts

Image processing

Transform theory

Image segmentation

Binary data

Data modeling

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