Unmixing Intimate Mixtures Using Bézier Surfaces

Due to the complex interaction of incident light with intimately mixed materials, the relationship between acquired reflectance spectra and the composition of materials is highly nonlinear. Spectral variability due to changes in illumination and acquisition conditions further complicates the unmixing procedure. In this work, we propose a method to accurately characterize a nonlinear simplex by a Bézier surface, by utilizing training samples. The fractional abundances of a test sample can be estimated by reconstruction of its reflectance spectrum on the Bézier surface. Moreover, the proposed method is made invariant to changes in the acquisition and illumination conditions. Experiments are conducted on simulated and real laboratory-generated mineral powder mixtures. The experimental results confirm the potential of the proposed methodology.