We have previously shown that it is possible to construct a coordinate system in the space of illumination spectra such that the coordinate vectors of the illuminants are located in a cone. Changes in the space of illuminants can then be described by an intensity related scaling and a transformation in the Lorentz group SU(1,1).In practice it is often difficult and expensive to measure these coordinate vectors. Therefore it is of interest to estimate the characteristics of an illuminant from an RGB image captured by a camera. In this paper we will investigate the relation between sequences of illuminants and statistics computed from RGB images of scenes illuminated by these illuminants.As a typical example we will study sequences of black body radiators of varying temperature. We have shown earlier that black body radiators in the mired parametrization can be described by one-parameter groups of the Lorentz group SU(1,1). In this paper we will show that this group theoretical structure of the illuminant space induces a similar structure in spaces of statistical descriptors of the resulting RGB images. We show this relation for mean vectors of RGB images, for RGB histograms and for histograms of images obtained by applying certain spatiospectral linear filters to the RGB images. As a result we obtain estimates of the color temperature of the illuminant from sequences of RGB images of scenes under these illuminants.
Thanh Bui, Reiner Lenz, Martin Solli, "Illumination Induced Changes in Image Statistics" in Proc. IS&T CGIV 2006 3rd European Conf. on Colour in Graphics, Imaging, and Vision, 2006, pp 48 - 53, https://doi.org/10.2352/CGIV.2006.3.1.art00010