In this manuscript we propose a method for the autonomous determination of endmembers in hyperspectral imagery based on recent theoretical advancements on lattice autoassociative memories. Given a hyperspectral image, the lattice algebra approach finds in a single-pass all possible candidate endmembers from which various affinely independent sets of final endmembers may be derived. In contrast to other endmember detection methods, the endmembers found using two dual canonical lattice matrices are geometrically linked to the data set spectra. The mathematical foundation of the proposed method is first described in some detail followed by application examples that illustrate the key steps of the proposed lattice based method.