Piecewise-constant reflectance spectra, their autocorrelation, and their application in camera characterisation

We introduce the concept of piecewise-constant reflectance spectra as a tool for modelling autocorrelation statistics in the context of reflectance and colour-signal spectra. By representing reflectance spectra as piecewiseconstant
functions, we show that the corresponding spectral reflectance autocorrelation matrices are very similar to those found for real datasets and, moreover, we provide a tuning parameter so that the fit is almost perfect. We apply the idea in the context of camera characterisation and demonstrate that algorithms founded on these new piecewise-constant reflectances, via their autocorrelation, deliver excellent colour calibration, on par with using the measured reflectances themselves. The importance of this work is that we can exactly characterise the set of all piecewise constant reflectances, which is useful because we cannot measure all possible reflectances that might be encountered in the real world.