Comparison of χ2 and κ statistics in finding signal and picture periodicity

Two statistical measures, based on contingency tables, were compared in trying to reveal the periodic or quasiperiodic structure of a texture from its cooccurrence histogram: the χ² and the κ statistics. Both are sensitive to periodicity, but the κ statistic is clearly better in the sense that the χ² can attain high values for displacements quite different from the actual period, as long as the cooccurrence histogram shows a specific structure associating the two relevant variables. If periodicity is the property looked for, then statistical agreement, measured by the κ statistic, is the property that will best reveal it