Analytic model for the autocorrelation matrix based on piecewise-functional spectra, and its application in camera characterization

The concept of piecewise-functional spectra is introduced as a tool for modeling autocorrelation statistics in the context of reflectance and color-signal spectra. By considering an infinite set of such spectra that satisfy any target statistics, a closed form expression is obtained for the autocorrelation matrix. Significantly, the model only contains a single tuning parameter that enables the degree of correlation to be adjusted. Interestingly, if the autocorrelation statistics do not vary as a function of wavelength, then the model spectra become piecewise constant. The utility of the idea is demonstrated in the context of camera color characterization. Here a model of the reflectance spectra can be exactly characterized, which is important because it is not possible to measure or numerically calculate all reflectances that might be encountered in the real world.