Unraveling N-FINDR: A generalization of geometrical linear unmixing approaches under the pure pixel assumption

Hyperspectral unmixing is an important task in hyperspectral image analysis, aiming to decompose mixed pixels into pure spectral signatures. Among existing unmixing approaches, the N-FINDR algorithm is one of the most widely used methods. However, over time, multiple implementations have emerged in the literature, often differing in parameter choices, algorithmic details, and operational assumptions. This lack of standardization has led to confusion and difficulties in comparing studies. As a result, the field lacks a unified and unambiguous formulation of the N-FINDR algorithm that clearly defines its principles, its relationship to closely related methods, and enables reproducible research.

We introduce a generalized and standardized formulation of the N-FINDR algorithm that explicitly defines its geometric principles, parameter choices, and operational steps. Ambiguous abbreviations commonly used in prior descriptions are replaced with explicit parameter values, enabling transparent interpretation and consistent implementation. The proposed framework clarifies the relationship between N-FINDR and other pure-pixel endmember extraction methods, particularly Vertex Component Analysis (VCA), highlighting shared assumptions and key differences. Comprehensive benchmarking experiments evaluate the influence of algorithmic variants, initialization strategies, and parameter settings on extraction performance. Based on this analysis, we identify best-practice configurations that provide robust and reproducible results across datasets. To facilitate adoption, we release open-source Python and R packages implementing the recommended variants, allowing both expert and non-expert users to apply N-FINDR reliably without detailed algorithmic tuning. Significance and Novelty. This work resolves long-standing ambiguities surrounding the N-FINDR algorithm by providing a standardized, transparent, and reproducible formulation. By clarifying its relationship to other pure-pixel methods and establishing best practices through systematic benchmarking, the study improves the reliability of hyperspectral unmixing research. The availability of open-source implementations further lowers the barrier to entry, enabling broader and more consistent use of N-FINDR across the hyperspectral imaging community.