Exponential image enhancement in daytime fog conditions

The images captured in fog conditions have degraded contrast, that 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, that takes 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 non-linear 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 comparing to 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 image enhancement in both homogeneous and heterogeneous fog conditions. Our algorithm is able to perform image enhancement in real time for both color and gray scale images.