A Comprehensive Evaluation of Spectral Distance Functions and Metrics for Hyperspectral Image Processing Distance functions are at the core of important data analysis and processing tools, e.g., PCA, classification, vector median filter, and mathematical morphology. Despite its key role, a distance function is often used without careful consideration of its underlying assumptions and mathematical construction. With the objective of identifying a suitable distance function for hyperspectral images so as to maintain the accuracy of hyperspectral image processing results, we compare existing distance functions and define a suitable set of selection criteria. Bearing in mind that the selection of distance functions is highly related to the actual definition of the spectrum, we also classify the existing distance functions based on how they inherently define a spectrum. Theoretical constraints and behavior, as well as numerical tests are proposed for the evaluation of distance functions. With regards to the evaluation criteria, Euclidean distance of cumulative spectrum (ECS) was found to be the most suitable distance function.