Nonlinear Spectral Unmixing Using Bézier Surfaces

Accurate estimation of the fractional abundances of intimately mixed materials from spectral reflectances is generally hard due to a highly nonlinear relationship between the measured spectrum and the composition of the material. Changes in the acquisition and the illumination conditions cause variability in the spectral reflectance, further complicating the spectral unmixing procedure. In this work, we propose a methodology for unmixing intimate mixtures that can tackle both nonlinearity and spectral variability. A supervised approach is proposed that characterizes the nonlinear data manifolds by high-dimensional Bézier surfaces. To deal with spectral variability, a manifold transformation procedure is designed. To generate Bézier surfaces, training samples are required that are uniformly distributed throughout the data manifold. For this, we recently generated a hyperspectral dataset of intimate mineral powder mixtures by homogeneously mixing five different clay powders (Kaolin, Roof clay, Red clay, mixed clay, and Calcium hydroxide) in laboratory settings. In total 330 samples (325 mixtures and five pure materials) were prepared. The ground fractional abundances of these mixtures uniformly cover the 5-D probability simplex. The spectral reflectances of these samples were acquired by multiple sensors with a large variation in sensor types, platforms, and acquisition conditions. Experiments are conducted both on simulated and real intimate mineral powder mixtures. Comparison with a number of unsupervised unmixing methods demonstrates the potential of the proposed approach.