Associative morphological memories for endmember determination in spectral unmixing

Autoassociative morphological memories (AMM) are a construct similar to hopfield autoassociatived memories defined on the (R, +, v, ∧) lattice algebra. Unlimited storage and perfect recall of noiseless real valued patterns has been proved for AMMs. However AMMs suffer from sensitivity to specific noise models, that can be characterized as erosive and dilative noise. On the other hand, spectral unmixing of hyperspectral images needs the prior definition of a set of endmembers, which correspond to material spectra lying on vertices of the minimum convex region covering the image data. These vertices can be characterized as morphologically independent patterns. We present a procedure based on the AMM noise sensitivity for endmember detection based on this characterization.