Water into wine: converting scanner RGB to tristimulus XYZ

A simple method of converting scanner (RGB) responses to estimates of object tristimulus (XYZ) coordinates is to apply a linear transformation to the RGB values. The transformation parameters are selected subject to minimization of some relevant error measure. While the linear method is easy, it can be quite imprecise. Linear methods are only guaranteed to work when the scanner sensor responsivities are within a linear transformation of the human color-matching functions. In studying the linear transformation methods, we have observed that the error distribution between the true and estimated XYZ values is often quite regular: plotted in tristimulus coordinates, the error cloud is a highly eccentric ellipse, often nearly a line. We will show that this observation is expected when the collection of surface re ectance functions is well-described by a low-dimensional linear model, as is often the case in practice. We will discuss the implications of our observation for scanner design and for color correction algorithms that encourage operator intervention.