Nonparametric statistical tests for exploration of correlation and nonstationarity in images

This work proposes two statistical-based techniques to quantify (with confidence) whether random 2D data (images) are correlated or nonstationary. Traditionally, such exploratory data analysis techniques have been developed for 1D signals, such as EEG. This paper presents a new application of Mantel's test for clustering to examine spatial dependence and a novel 2D extension of the traditional 1D version of the reverse arrangements test to examine data nonstationary. Simulated data (correlated and nonstationary) were generated and subject to several rotations, scales and translations, in order to test the robustness of the techniques. Mantel's test for clustering correctly classified the images as correlated for 100% of the cases (including those with rotations, scales and translations (RSTs)). For the 2D extension of the reverse arrangements test, the linear trend analysis correctly found 15/16 regions to have pixel-wise nonstationarity, and the nonlinear trend analysis correctly classified nonstationarity in all but two cases (14/16) (for all RSTs). As a result of the high classification rates, the techniques are relatively invariant to changes in RST. These two statistical tests have a variety of applications in medical imaging (i.e. modeling), and are discussed in this work. An additional application of the work is presented in the end, demonstrating the possibility that such test statistics may be used as features to classify different textures.