Unmixing multiple intimate mixtures using manifold clustering

In this paper, we will show that the Hapke model, a well known radiative transfer scattering model for intimate mixtures, when considered as a nonlinear function of endmember grain sizes, abundances, illumination and viewing angles, can be represented geometrically as a low dimensional manifold with a gentle curvature. In this scenario, we can represent the data cloud of a scene composed by several intimate mixtures with shared endmembers as a set of intersecting manifolds. We propose a manifold-clustering based method to identify the different intimate mixtures by learning the optimal geometrical separation of a linear approximation of the corresponding manifolds. Unmixing is then performed separately in each discovered cluster by a modification of the ISOMAP embedding that takes into account that the Hapke model produces data clouds exhibiting an increasing density gradient from bright to dark endmembers. Given the lack of availability of ground truth and datasets of known intimate mixture measurements, we test the algorithm on several simulated datasets generated using a version of the Hapke model.