A Geometric Unmixing Concept for the Selection of Optimal Binary Endmember Combinations

One of the major issues with spectral mixture analysis remains the lack of ability to properly account for the spectral variability of endmembers (EMs). EM variability is most often addressed using large spectral libraries incorporating the variability present in the image. We propose a new geometric-based methodology to efficiently evaluate different binary EM combinations. Our approach selects the best EM combination prior to unmixing, building upon the equivalence between the reconstruction error in least squares unmixing and spectral angle minimization in geometric unmixing. This geometric approach is tested on both a simulated data set based on field measurements and a HyMap image. It is demonstrated that selecting the best EM combination for a pixel based on the angle minimization provided identical results compared with using the projection distance or reconstruction error. It also has the additional benefit of reducing the computation time due to the simplicity of the angle calculations.