Color sensors in scanners and color copiers are not colorimetric—RGB values are not a linear transformation away from device-independent XYZ tristimulus values. For a given set of targets or dyes one can readily find a best linear transform or use interpolation. However, when the possible targets are unknown, a data-independent transform is needed.Here, we set out a very simple linear transform for forming XYZ from RGB, developed in analogy with a well-known solution for the color constancy problem in computer vision, based on using narrow-band sensors. In a scanner, we know the illuminant. Therefore the color constancy paradigm—illumination-independent colors—is not applicable. Instead, we change filters—from RGB to XYZ. The von Kries adaptation form of the color constancy solution can then apply if we can “sharpen” both the RGB sensors and the XYZ color-matching functions. Recently, we developed just such a “sharpening” basis transform: most of the sensitivity of the new possibly partly negative sensors is isolated in a particular wavelength interval. Here we “sharpen” both sensor sets; after dividing by sharpened white-spot values an inverse transform results in recovered XYZ values. Applying the method to 462 Munsell chips yields a median CIELAB error of only 3 units for two different systems.