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1. EXPONENTIAL CONTRAST RESTORATION IN FOG CONDITIONS FOR DRIVING
ASSISTANCE
ABSTRACT
The images captured in fog conditions have degraded contrast, which makes current
image processing applications sensitive and error prone. We propose in this paper an efficient
single-image enhancement algorithm suitable for daytime fog conditions and, based on an
original mathematical model, for computing the atmospheric veil, taking into account the
variation in fog density to the distance. This model is inspired by the functions that appear in
partition of unity in the differential geometry field. When observing images captured in fog
conditions, usually the fog has a very low density in front of the camera and this density has a
nonlinear increase with the distance, such that objects are no longer visible at greater distances.
By using our mathematical model, we are able to obtain superior reconstructions of the original
fog-free image when compared with traditional methods. Another advantage of our method is the
ability to adapt the model in accordance to the density of the fog. A quantitative and qualitative
evaluation is performed on both synthetic and real camera images. This evaluation proves that
our mathematical model is more suitable for contrast restoration in both homogeneous and
heterogeneous fog conditions. Our algorithm is able to perform contrast restoration in real time
for both color and grayscale images.