Endmembers as Directional Data for Robust Material Variability Retrieval in Hyperspectral Image Unmixing

Hyperspectral image unmixing is a source separation problem aiming at recovering the spectra of the pure materials of the observed scene (called endmembers), as well as their relative proportions in each pixel of the image (called abundances). The variability of the materials has recently received a lot of attention in the community. In particular, a consequent number of models and algorithms have been proposed to estimate pixel-wise endmembers to account for their variability. These algorithms often rely on classical endmem-ber extraction algorithms to provide reference spectra. In difficult scenarios with shadows and significant variability these algorithms may fail. In this paper, we address this issue in the Extended Linear Mixing Model framework by considering that an endmember is a direction in the feature space, rather than a single point. Under this paradigm, we show that using k- means clustering with the cosine similarity outperforms geometric endmember extraction algorithms. We also design an algorithm to refine the estimation of the endmem-ber directions, and to account for both illumination and intrinsic variability effects. We show the potential of the proposed algorithm on a synthetic dataset using real world spectra with variability, and a challenging real dataset of a natural scene.