Gaussian mixture model based approach to anomaly detection in multi/hyperspectral images

Anomaly detectors reveal the presence of objects/materials in a multi/hyperspectral image simply searching for those pixels whose spectrum differs from the background one (anomalies). This procedure can be applied directly to the radiance at the sensor level and has the great advantage of avoiding the difficult step of atmospheric correction. The most popular anomaly detector is the RX algorithm derived by Yu and Reed. It is based on the assumption that the pixels, in a region around the one under test, follow a single multivariate Gaussian distribution. Unfortunately, such a hypothesis is generally not met in actual scenarios and a large number of false alarms is usually experienced when the RX algorithm is applied in practice. In this paper, a more general approach to anomaly detection is considered based on the assumption that the background contains different terrain types (clusters) each of them Gaussian distributed. In this approach the parameters of each cluster are estimated and used in the detection process. Two detectors are considered: the SEM-RX and the K-means RX. Both the algorithms follow two steps: first, 1) the parameters of the background clusters are estimated, then, 2) a detection rule based on the RX test is applied. The SEM-RX stems from the GMM and employs the SEM algorithm to estimate the clusters' parameters; instead, the K-means RX resorts to the well known K-means algorithm to obtain the background clusters. An automatic procedure is defined, for both the detectors, to select the number of clusters and a novel criterion is proposed to set the test threshold. The performances of the two detectors are also evaluated on an experimental data set and compared to the ones of the RX algorithm. The comparative analysis is carried out in terms of experimental Receiver Operating Characteristics