Using endmembers as a coordinate system in hyperspectral imagery

The linear mixing model (LMM) is a well-known and useful method for decomposing spectra in a hyperspectral image into the sum of their constituents, or endmembers. Mathematically, if the spectra are represented as n-dimensional vectors, then the LMM implies that the set of endmembers defines a basis or coordinate system for the set of spectra. Because the endmembers, themselves are generally not orthogonal, the geometry (distances, difference angles, etc.) is changed by moving from band space to endmember space. We explore some of the differences between the two coordinate systems, and show in particular that the difference in angle measurements leads to an improved method for subpixel target detection.