Spectral recovery using polynomial models

If digital cameras and scanners are to be used for colour measurement it is necessary to correct their device responses to device-independent colour co-ordinates, such as CIE tristimulus values. In order to do this it is sufficient to recover the underlying spectral reflectance functions from a scene at each pixel. Traditionally, linear methods are used to transform device responses to reflectance values. Recently, however, several non-linear methods have been applied to this problem, including generic methods such as neural networks, more novel approaches such as sub-manifold approximation and approaches based upon quadratic programming. In this paper we apply polynomial models to the recovery of reflectance. We perform a number of simulations with both tri-chromatic and multispectral imaging systems to determine their accuracy and generalisation performance. We find that, although higher order polynomials seem to be superior to linear methods in terms of accuracy, the generalisation performance for the two methods is approximately equivalent. This suggests that the advantage of polynomial models may only be seen when the training and test data are statistically similar. Furthermore, the experiments with multispectral systems suggest that the improvement using high order polynomials on training data is reduced when the number of sensors is increased.