Endmember detection using graph theory

In this paper, we propose a new nonlinear approach which uses graphs for detecting endmembers in hyperspectral images. Endmembers are defined as the purest points of the image and lie on the boundary of the data cloud. The image is modeled by a graph and in order to reduce the effects of noise and artifacts existent in the image, the superpixel representation is used instead of pixel representation. Superpixels are the image segments with locally contiguous pixels. The nodes of the graph are the mean spectra of the superpixels and some similarity between each pair of the nodes defines their connectivity to each other. Since the endmembers are the extreme points of the data cloud, we use graph theoretic quantities to discriminate them from the central points in the data cloud. For the validation of the introduced method, we apply this approach to some real hyperspectral images and present the results of applying the method to one image.