Spectral Signature Ranking based on Lexicographic Ordering of Autocorrelation Function Values

We model the spectral signatures or spectral reflectance curves representing colors as power spectral density (PSD) functions, instead of considering them signals. Assuming that colors are generated by stationary random processes and deploying the Wiener-Khinchin theorem, we link the PSD of a color, thus the physical measurement of reflected or radiant energy, to the information provided by such spectrum. From the PSD, through the inverse Fourier transform, we recover the autocorrelation function of the corresponding random process. We propose ranking the spectral signatures of colors by imposing a lexicographic ordering of the autocorrelation function values. Such ranking can be deployed for the construction of nonlinear operators like morphological ones. We validate our approach on reference colors of a standard color set widely-used in colorimetry. We show the usefulness of our approach by computing morphological profiles for pixel classification using a widely-known hyperspectral image.