Variational Bayesian Method for Retinex

In this paper, we propose a variational Bayesian method for Retinex to simulate and interpret how the human visual system perceives color. To construct a hierarchical Bayesian model, we use the Gibbs distributions as prior distributions for the reflectance and the illumination, and the gamma distributions for the model parameters. By assuming that the reflection function is piecewise continuous and illumination function is spatially smooth, we define the energy functions in the Gibbs distributions as a total variation function and a smooth function for the reflectance and the illumination, respectively. We then apply the variational Bayes approximation to obtain the approximation of the posterior distribution of unknowns so that the unknown images and hyperparameters are estimated simultaneously. Experimental results demonstrate the efficiency of the proposed method for providing competitive performance without additional information about the unknown parameters, and when prior information is added the proposed method outperforms the non-Bayesian-based Retinex methods we compared.