Bayesian Pairwise Comparison of High-Dimensional Images

A fundamental task in the automated analysis of images is the development of effective image pair comparison techniques. For two high-dimensional images, a statistical method must automatically label them as "similar" or "different" depending on whether random error and spatial dependencies could account for the pixel-wise differences. We develop a Bayesian strategy by constructing a novel extension of Dirichlet processes called the spatial random partition model (sRPM). The process groups spatially proximal image pixels with similar intensities into clusters, thereby achieving dimension reduction in the large number of pixels. Next, we apply the sRPM-based analytical procedure to compare two images. The image comparison problem is formulated as a hypothesis test involving a univariate metric adaptive to spatial correlations and robust to random variability in the pixel intensities. To handle the computational burden, we foster a two-stage technique for MCMC analysis and hypothesis testing of image pairs. A simulation study analyzes artificial datasets and finds compelling evidence for the high accuracy of sRPM in image comparison. We demonstrate the effectiveness of the technique by statistically analyzing satellite image data.