Statistical measures of two dimensional point set uniformity

Three different classes of statistical measures of uniformity, namely, discrepancy, point-to-point measures and volumetric measures, are described and compared in this paper. Correlation studies are carried out to compare their performance in discerning uniformity of random and quasi-random point sets with respect to human perception of uniformity. Some of the measures reported in the literature are found to be able to characterize and rank very limited class of point sets correctly. A new approach to better characterize uniformity based on the physical analogy of potential energy is proposed. An approximate closed-form expression measuring the average uniformity of point set generated by spatial Poisson process is also derived theoretically. A novel application in signal processing is presented and extensive simulations are carried out to corroborate the validity of the proposed technique.