Graph-based identification of boundary points for unmixing and anomaly detection

In this paper, we propose a new approach based on graphs which can be used for detecting both endmembers and anomalies present in hyperspectral images. After a preliminary oversegmentation of the image using superpixels, the superpixel segment averages are considered as the nodes of graph. A measure of spectral similarity (Euclidean distance) is used as edge weights. Superpixel segmentation is employed to reduce the effects of noise and artifacts existent in CRISM images and also to reduce the number of the points to be analyzed. Graph theoretic quantities are used to identify the points which lie on the boundary of the data cloud. Endmembers and anomalies belong to the set of the boundary points. Endmembers are the points on the convex hull and anomalies which are outliers in the data cloud can be found by ranking out of the boundary points set. This method can be applied to the images without imposing any assumptions on the type of mixing or the shape of the data cloud. We validate our approach by applying the method to some hyperspectral images and compare the endmembers and anomalies extracted by our approach and the ones identified by scientists.