Two lattice computing approaches for the unsupervised segmentation of hyperspectral images

Endmembers for the spectral unmixing analysis of hyperspectral images are sets of affinely independent vectors, which define a convex polytope covering the data points that represent the pixel image spectra. Strong lattice independence (SLI) is a property defined in the context of lattice associative memories convergence analysis. Recent results show that SLI implies affine independence, confirming the value of lattice associative memories for the study of endmember induction algorithms. In fact, SLI vector sets can be easily deduced from the vectors composing the lattice auto-associative memories (LAM). However, the number of candidate endmembers found by this algorithm is very large, so that some selection algorithm is needed to obtain the full benefits of the approach. In this paper we explore the unsupervised segmentation of hyperspectral images based on the abundance images computed, first, by an endmember selection algorithm and, second, by a previously proposed heuristically defined algorithm. We find their results comparable on a qualitative basis.