NFINDR

N-FINDR is an algorithm used in hyperspectral imaging to identify endmembers, the pure spectral signatures that compose mixed pixels. It is based on the linear mixing model, where each pixel is assumed to be a convex combination of endmember spectra.

The core idea is to find the set of endmembers that maximizes the volume of the simplex formed by those endmembers in the spectral space. Because true endmembers tend to lie at the extreme points of the data cloud, maximizing the simplex volume tends to select spectra that are on the convex hull of the observed pixels. In practice, the algorithm evaluates candidate sets of endmembers and keeps the one that yields the largest simplex volume, often implemented with a sequential or heuristic search to manage computational cost.

NFINDR is typically applied after reducing dimensionality (for example with PCA) to mitigate noise and to limit the number of bands considered. It also benefits from data preprocessing such as noise filtering and normalization. The method is sensitive to noise, outliers, and nonpure pixels, and its performance can degrade under strong spectral variability or nonlinear mixing.

Because of its intuitive geometric basis and its efficiency with early-pixel purity assumptions, NFINDR has become a foundational technique in hyperspectral endmember extraction. It has inspired numerous variants and improvements focused on speed, robustness, and integration with later unmixing methods, and remains a reference point in the study of convex-hull approaches to spectral unmixing.