Detection of Groups of Point Objects in Spaces of Different Dimensions Based upon Spatial Compactness Criterion

Abstract

Images of groups of point objects (GPOs) specified in one-, two-, and three-dimensional spaces are considered. We show that the introduction of an associated continuous image (ACI) as an abstract mathematical object relating the elements of the GPO makes possible use of a measure of spatial compactness invariant to the configuration of the GPO. The problem of detecting compact GPOs, including the partially disguised, is reduced to a computationally simple observation-invariant procedure for detecting contrasting areal objects or a structural analysis of a graph of hierarchical grouping of the elements of the GPOs in the scene, which gives similar results. We then find the GPO detection characteristics for various observation conditions.