White-point preserving color correction

To characterize color values measured by color devices (e.g. scanners, color copiers and color cameras) in a device–independent fashion these values must be transformed to colorimetric tristimulus values. Often it is assumed that RGBs are approximately linearly related to XYZs and so this transformation is determined by least–squares (LS) linear regression. While the LS method is guaranteed to minimize the residual squared error it makes no a priori statement about which colors will be mapped well and which will be mapped poorly. However, we argue that such a statement must be made. In particular because it is important to preserve the white and the gray-scale in color reproduction, we argue that achromatic colors should be preserved in color correction. This argument led us to develop a new regression procedure: the white-point preserving least-squares fit (WPPLS). As the name might suggest, this method finds the linear transform which maps RGBs to XYZs such that the residual squared error is minimized subject to the constraint that white and grays are preserved. Of course, by definition, the WPPLS regression must, in terms of squared error, deliver poorer color correction compared with the LS procedure; but, squared error need not necessarily correlate with perceived visual error. Indeed, we present a number of simulation experiments which show that theWPPLS procedure performs as well or better than the LS regression. These results provide experimental confirmation of the privileged status of white in visual perception and color reproduction.