Daytime fog detection and density estimation with entropy minimization

Caraffa, L.; Tarel, J. P. · 2014 · OpenAlex-citations

DOI: 10.5194/isprsannals-ii-3-25-2014

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Summary

This paper addresses the challenge of detecting fog and estimating its density in outdoor scenes, specifically for applications involving moving cameras such as autonomous vehicles. Fog significantly reduces visibility and degrades image processing performance. While defogging algorithms exist, they require prior detection of fog to avoid enhancing noise. Existing fog detection methods are largely limited to static cameras or rely on specific scene assumptions, such as the presence of road markings or a planar road surface. The authors propose a generic, fast algorithm based on entropy minimization that works with stereo camera pairs, enabling accurate fog characterization even when the sensor is in motion. The method utilizes stereo vision to obtain a depth map of the scene. The algorithm first estimates the intensity of the sky ($I_s$) by identifying high-contrast regions using the Sobel operator. It then segments the image into regions of constant albedo with sufficient depth variation, rejecting fronto-parallel or small regions. For a range of possible extinction coefficients ($\beta$), the algorithm restores the image intensity using Koschmieder’s law. The correct $\beta$ is identified as the value that minimizes the Shannon entropy of the restored intensity distributions within the selected regions. This approach ensures that homogeneous areas in the scene appear uniform after restoration, indicating accurate fog removal. The method requires only accurate depth information up to a critical distance, rather than the entire scene range. The proposed algorithm was evaluated on both static and moving sensor scenarios. For static sensors, the authors used the Matilda database, which contains images with ground-truth visibility measurements from a visibility meter. Results showed that the method achieved accuracy comparable to physical visibility meters, with mean relative errors as low as 7.1% when limiting the depth range to 50 meters. For moving sensors, the algorithm was tested on the Frida3 synthetic stereo database. When using ground-truth depth maps, the mean relative error was 4.67%. When using depth maps generated by a stereo reconstruction algorithm, the error increased to 16.03%, yet remained acceptable for practical applications. The experiments demonstrated that the entropy minimum closely aligns with ground-truth $\beta$ values across various weather conditions. The significance of this work lies in providing a robust, real-time capable solution for fog detection and visibility estimation in dynamic environments. By relying on entropy minimization over segmented regions, the method avoids the need for specific scene structures or full-range depth accuracy. This makes it particularly suitable for vehicular applications where obstacles may occlude distant parts of the scene and where rapid processing is essential. The ability to estimate visibility distance accurately using low-cost stereo cameras enhances the reliability of computer vision systems in adverse weather conditions.

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• weather rain fog snow