Convex geometry based estimation of number of endmembers in hyperspectral images

Hyperspectral unmixing is a process of decomposing the hyperspectral data cube into endmember signatures and their corresponding abundance maps. For the unmixing results to be completely interpretable, the number of materials (or endmembers) present in that area should be known a priori, which however is unknown in practice. In this work, we use hyperspectral data geometry and successive endmember estimation strategy of an endmember extraction algorithm (EEA) to develop two novel algorithms for estimating the number of endmembers, namely geometry based estimation of number of endmembers - convex hull (GENE-CH) algorithm and affine hull (GENE-AH) algorithm. The proposed GENE algorithms estimate the number of endmembers by using Neyman-Pearson hypothesis testing over the endmembers sequentially estimated by an EEA until the estimate of the number of endmembers is obtained. Monte- Carlo simulations demonstrate the efficacy of the proposed GENE algorithms, compared to some existing benchmark methods for estimating number of endmembers.