Spectral calibration of digital cameras based on the spectral data of commercially available calibration charts is an illconditioned problem which has an infinite number of solutions. To improve upon the estimate, different constraints are commonly employed. Traditionally such constraints include: nonnegativity, smoothness, uni-modality and that the estimated sensors results in as good as possible response fit.In this paper, we introduce a novel method to solve a general ill-conditioned linear system with special focus on the solution of spectral calibration. We introduce a new approach based on metamerism. We observe that the difference between two metamers (spectra that integrate to the same sensor response) is in the null-space of the sensor. These metamers are used to robustly estimate the sensor's null-space. Based on this nullspace, we derive projection operators to solve for the range of the unknown sensor. Our new approach has a number of advantages over standard techniques: It involves no minimization which means that the solution is robust to outliers and is not dominated by larger response values. It also offers the ability to evaluate the goodness of the solution where it is possible to show that the solution is optimal, given the data, if the calculated range is one dimensional.When comparing the new algorithm with the truncated singular value decomposition and Tikhonov regularization we found that the new method performs slightly better for the training set with noticeable improvements for the test data.
Ali Alsam, Reiner Lenz, "Calibrating Color Cameras using Metameric Blacks" in Proc. IS&T CGIV 2006 3rd European Conf. on Colour in Graphics, Imaging, and Vision, 2006, pp 75 - 80, https://doi.org/10.2352/CGIV.2006.3.1.art00015