Factorizing Scene Albedo and Depth from a Single Foggy Image

Atmospheric conditions induced by suspended particles, such as fog and haze, severely degrade image quality. Restoring the true scene colors (clear day image) from a single image of a weather-degraded scene remains a challenging task due to the inherent ambiguity between scene albedo and depth. In this paper, we introduce a novel probabilistic method that fully leverages natural statistics of both the albedo and depth of the scene to resolve this ambiguity. 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. We show that we may exploit natural image and depth statistics as priors on these hidden layers and factorize a single foggy image via a canonical Expectation Maximization algorithm with alternating minimization. Experimental results show that the proposed method achieves more accurate restoration compared to state-of-the-art methods that focus on only recovering scene albedo or depth individually.