Coping with mixtures of backgrounds in a sliding dual window anomaly detection algorithm

Without prior information about the spectral signature of the desired targets in hyper- or multi-spectral images, detection algorithms look for those pixels that deviate most strongly from the statistics of their surrounding backgrounds. If we presume that the distribution of the background signatures is multivariate Gaussian, then the most common anomaly test is the RX algorithm which is based on the Mahalanobis distance. We have implemented an anomaly detection algorithm based on Triple Concentric Sliding Windows (TCSW) to perform a local RX algorithm between the inner window and each segment that appears in the outer window. The dimension of the inner window is designed to fit the size of the desired targets; in this way, we integrate both spectral and spatial properties. When the inner window contains a random mixture of backgrounds, the score of the anomaly test is rather high because the mean of the mixture is far from each of the background components. In order to deal with these mixture situations, we develop two modified versions of the RX algorithm (ISMPRX, SMPRXMix) that take into consideration the possibility of segment mixture in the inner window. The results show significant improvement in the anomaly detection performance.