Color Calibration of a Colorimetric Scanner Using Non-Linear Least Squares

Abstract

In this paper we present a technique to improve the calibration of a colorimetric scanner by employing an affine model in conjunction with non-linear least squares fitting. In the affine model, the transformation from image RGB values to CIE XYZ values is specified as a multiplication with a 3×3 matrix, M s, followed by the addition of a constant vector, K. This model allows one to first transform the image RGB values to CIE XYZ values under a specified illuminant and then to convert these XYZ values to the appropriate RGB or CMYK values for viewing on different output devices. The precise values of the entries in the matrix M s and vector K are determined through a non-linear least squares procedure, in which the total CIE ΔE between the ideal XYZ and predicted XYZ values of a calibration chart is minimized. We interpret the role of the constant term K to be a subtraction of the white of the illuminating source.