endmember

An endmember is a theoretically pure component used to describe mixtures in fields such as spectroscopy, remote sensing, and geochemistry. In hyperspectral imaging and reflectance spectroscopy, the spectrum recorded for a pixel is often treated as a mixture of the spectra of several endmembers, each weighted by an abundance that reflects its fractional contribution to the pixel.

Endmembers can be real materials measured in situ or in the laboratory, or spectral signatures derived directly from image data by endmember extraction algorithms. Common approaches aim to identify a small set of endmembers that maximizes the separability or the geometric volume of the data's convex hull in spectral space.

In the linear mixing model, the observed spectrum R(λ) is approximated as R(λ) ≈ ∑ a_i e_i(λ), where e_i(λ) is the endmember spectrum, a_i ≥ 0 are abundances, and ∑ a_i = 1. This framework underpins many unmixing techniques used to estimate both the endmember signatures and their abundances.

Applications include mineral and vegetation mapping, soil characterization, and planetary remote sensing. Endmember modeling is also used in chemometrics for mixtures of chemical spectra and in material science to decompose composite spectra.

Limitations include spectral variability within a material, illumination and viewing geometry effects, and intimate or nonlinear mixing that violates the linear assumption. Consequently, endmembers may be treated as variable or replaced by libraries of candidate spectra, and non-linear or partially constrained models are used when appropriate.