We present a Bayesian approach to color constancy which utilizes a non- Gaussian probabilistic model of the image formation process. The pa- rameters of this model are estimated directly from an uncalibrated image set and a small number of additional algorithmic parameters are chosen using cross validation. The algorithm is empirically shown to exhibit RMS error lower than other color constancy algorithms based on the Lambertian surface reflectance model when estimating the illuminants of a set of test images. This is demonstrated via a direct performance comparison utilizing a publicly available set of real world test images and code base.

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model Gaussian marginal distributions. To model non-Gaussian data, a GP can be warped by a nonlinear transformation (or warping) as performed by warped GPs (WGPs) and more computationally-demanding alternatives such as Bayesian WGPs and deep GPs. However, the WGP requires a numerical approximation of the inverse warping for prediction, which increases the computational complexity in practice. To sidestep this issue, we construct a novel class of warpings consisting of compositions of multiple elementary functions, for which the inverse is known explicitly. We then propose the compositionally-warped GP (CWGP), a non-Gaussian generative model whose expressiveness follows from its deep compositional architecture, and its computational efficiency is guaranteed by the analytical inverse warping. Experimental validation using synthetic and real-world datasets confirms that the proposed CWGP is robust to the choice of warpings and provides more accurate point predictions, better trained models and shorter computation times than WGP.

A Gaussian process (GP) [1] is a prior distribution over functions with a support that includes a wide class of phenomena via the design of its mean and covariance functions, the parameters of which provide meaningful interpretation of the process at hand. Beyond regression [2], GPs have been extensively used in the last two decades for classification [3], density estimation [4], filter design [5], model identification [6] and optimisation [7]. In general terms, all these generative models have two stages: The latent process is modelled as a GP and the observation is modelled (conditional to the latent process) as a non-Gaussian variable. This class of models is referred to as GP with non-Gaussian likelihood, or as Generalised GPs. These usually consider likelihood functions from the exponential family such as the Laplace, Poisson, beta and gamma distributions [8]. A well-known example is the GP classification model, where the classes are represented by the output of an activation neuron into which a latent GP is fed. A slightly different approach to non-Gaussian models, which is not constrained to the exponential family, is the warped GP (WGP, [9]). The WGP models non-Gaussian data by assuming that there is a transformation φ such that the observations can be passed through φ to yield a GP, therefore, the likelihood function of this model is not designed directly but, rather, induced by the transformation (a.k.a.