A Geometric view of Fast Gram Determinant-Based Endmember Extraction Algorithm for Hyperspectral Imagery

Endmember determination is a key step of spectral unmixing, which decomposes a mixed pixel into endmembers and corresponding fractional abundances for hyperspectral imagery. So far, convex geometry-based endmember determination methods have attracted much attention due to their clear physical meaning and light computational burden. Recently, a Fast Gram Determinant-based Algorithm (FGDA) has been proposed as an efficient endmember determination method for hyperspectral imagery. In this letter, we further implement the derivation of endmember score index (ESI) defined in FGDA. From the algebra and geometric view, we find interestingly that the ESI is actually the height of a new vertex to the hyperplane or simplex linear spanned by previously found endmembers (base), and essentially the FGDA is equivalent to the Automatic Target Generation Process (ATGP) when their initial condition is the same.