Nonlinear Hyperspectral Unmixing With Graphical Models

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In optical remote sensing, phenomena such as multiple scattering, shadowing, and spatial neighbor effects generate spectral reflectances that are nonlinear mixtures of the reflectances of the surface materials. Using hyperspectral images, the obtained spectral reflectances can be unmixed. We present a general method for creating nonlinear mixing models, based on a ray-based approximation of light and a graph-based description of the optical interactions. This results in a stochastic process which can be used to calculate path probabilities and contributions, and their weighted sum. In many cases, a closed-form equation can be obtained. We illustrate the approach by deriving several existing mixing models, such as linear, bilinear, and multilinear mixing (MLM) models popular in remote sensing, layered models for vegetation canopies, and intimate mineral mixtures. Furthermore, we use the proposed technique to derive a new mixing model, which extends the MLM model with shadowing. Experiments on artificial and real data show the positive traits of this model, which also demonstrates the power of the graphical model approach.