Bayesian Defogging

Atmospheric conditions induced by suspended particles, such as fog and haze, severely alter the scene appearance. Restoring the true scene appearance from a single observation made in such bad weather conditions remains a challenging task due to the inherent ambiguity that arises in the image formation process. In this paper, we introduce a novel Bayesian probabilistic method that jointly estimates the scene albedo and depth from a single foggy image by fully leveraging their latent statistical structures. Our key idea is to model the image with a factorial Markov random field in which the scene albedo and depth are two statistically independent latent layers and to jointly estimate them. We show that we may exploit natural image and depth statistics as priors on these hidden layers and estimate the scene albedo and depth with a canonical expectation maximization algorithm with alternating minimization. We experimentally evaluate the effectiveness of our method on a number of synthetic and real foggy images. The results demonstrate that the method achieves accurate factorization even on challenging scenes for past methods that only constrain and estimate one of the latent variables.