Image Distinguishability Analysis Testing through Principal Components and its Application to Hot Spot Scale Invariance

Images are common means to represent spatial property variations in physical systems, but comparing images is nuanced due to stochastic variations and spatial correlations, which are neglected in routine analyses like the Kolmogorov-Smirnov test. To this end, we develop an image distinguishability analysis (IDA) test that makes pixel-by-pixel comparisons between image-like datasets through a generalized distance metric in the principal component (PC) space. Based on the supported hypothesis that inherent stochasticity is represented by independent Normal behavior of the PCs, we derive a statistical distribution and criticality criterion to determine whether images are distinguishable from established baselines. We apply the IDA test on images generated from molecular dynamics simulations to demonstrate scale invariance in the complex patterns of a nonequilibrium process. The IDA test is notably general with diverse potential applications, including microstructure classification and change detection, uncertainty quantification of property fields, and model validation against high-fidelity simulations and experiments.