  White balancing is a fundamental step in the image processing pipeline. The
process involves estimating the chromaticity of the illuminant or light source
and using the estimate to correct the image to remove any color cast. Given the
importance of the problem, there has been much previous work on illuminant
estimation. Recently, an approach based on ensembles of univariate regression
trees that are fit using the squared-error loss function has been proposed and
shown to give excellent performance. In this paper, we show that a simpler and
more accurate ensemble model can be learned by (i) using multivariate
regression trees to take into account that the chromaticity components of the
illuminant are correlated and constrained, and (ii) fitting each tree by
directly minimizing a loss function of interest---such as recovery angular
error or reproduction angular error---rather than indirectly using the
squared-error loss function as a surrogate. We show empirically that overall
our method leads to improved performance on diverse image sets.
