Integrating the Space of Reflectance Spectra

Color imaging algorithms - such as color correction, spectral estimation and color constancy - are developed and validated with spectral reflectance data. However, the choice of the reflectance data set - used in development and tuning - not only affects the results of these algorithms but it also changes the ranking of the different approaches. We propose that this fragility is because it is difficult to measure/sample enough data to statistically represent the large number of degrees of freedom apparent in spectral reflectances. In this paper, we propose that the space of reflectance data should not be sampled but, rather, integrated. Specifically, we advocate that the convex closure of a reflectance data set - all convex combinations of all spectra - should be used instead of discrete reflectance samples. To make the integration computation tractable, we approximate these convex closures by their enclosing hyper-cube in a privileged coordinate system. We use color correction as an exemplar color imaging problem to demonstrate the utility of our approach.