Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Computing the discrepancy with applications to supersampling patterns
ACM Transactions on Graphics (TOG)
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Uniformity Testing Using Minimal Spanning Tree
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 4 - Volume 4
Polynomial Behavioural Modelling of Switched Capacitor Amplifiers
Analog Integrated Circuits and Signal Processing
Poisson Disk Point Sets by Hierarchical Dart Throwing
RT '07 Proceedings of the 2007 IEEE Symposium on Interactive Ray Tracing
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Improved upper bounds on the star discrepancy of (t,m,s)-nets and (t,s)-sequences
Journal of Complexity
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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.