Daytime fog detection and density estimation with entropy minimization

Abstract. Fog disturbs the proper image processing in many outdoor observation tools. For instance, fog reduces the visibility of obstacles in vehicle driving applications. Usually, the estimation of the amount of fog in the scene image allows to greatly improve the image processing, and thus to better perform the observation task. One possibility is to restore the visibility of the contrasts in the image from the foggy scene image before applying the usual image processing. Several algorithms were proposed in the recent years for defogging. Before to apply the defogging, it is necessary to detect the presence of fog, not to emphasis the contrasts due to noise. Surprisingly, few a reduced number of image processing algorithms were proposed for fog detection and characterization. Most are dedicated to static cameras and can not be used when the camera is moving. Daytime fog is characterized by its extinction coefficient, which is equivalent to the visibility distance. A visibility-meter can be used for fog detection and characterization, but this kind of sensor performs an estimation in a relatively small volume of air, and is thus sensitive to heterogeneous fog, and air turbulence with moving cameras. In this paper, we propose an original algorithm, based on entropy minimization, to detect fog and estimate its extinction coefficient by the processing of stereo pairs. This algorithm is fast, provides accurate results using low cost stereo camera sensor and, the more important, can work when the cameras are moving. The proposed algorithm is evaluated on synthetic and camera images with ground truth. Results show that the proposed method is accurate, and, combined with a fast stereo reconstruction algorithm, should provide a solution, close to real time, for fog detection and visibility estimation for moving sensors.