LabRGB : Evaluation of the weighting factors

Spectral distribution can be written as a linear combination of eigenvectors and the eigenvectors method gives the least estimation error, but eigenvectors depend on a sample selection of population and encoding values have no physical meaning. Recently reported LabPQR [1] is to convey physical values, but still is dependent on a sample selection of population. Thus, LabRGB [2] was proposed in 2007. LabRGB is to provide "sample selection of population" free spectral encoding/decoding methods. LabRGB consists of six unique trigonometric base functions and physically meaningful encoding values. LabRGB was applied to the real multispectral images and showed almost equal performance to traditional orthogonal eigenvector method in spectral estimation, and even better performance in colorimetric estimation. In this paper, the weighting factors of the base functions were examined in terms of their possible ranges. The numerical values are obtained by using a linear programming technique, and the results are also confirmed by using the Monte Carlo method. The results indicate that the possible ranges of six scores for six base functions are well within -80 to 80. The ranges thus obtained give a good clue for explicitly defining the bit depths of respective scores for the future applications and standardization.