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
recoverin...