# Fog rectification reference algorithm

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Muhammad Bilal on 14 Oct 2022
Hi, Could someone please direct me towards the reference/publication to justify the equations used in the fog rectification example?
Usually, Matlab examples cite reference works at the end of the documentation page but this one does not list any. I am curious because the equations seem to be quite different from what some well-known works in the literature use. Eg. the example seems to use the same factor for both airlight and transmission. What surprises me even more is that the example seems to work for certain images albeit after setting some empirically derived coefficients. Thanks

Bharathi Yogaraj on 18 Oct 2022
Here are references for Fog rectification example:
1. He, Kaiming. "Single Image Haze Removal Using Dark Channel Prior." Thesis, The Chinese University of Hong Kong. 2011.
2. Dubok, et al. "Single Image Dehazing with Image Entropy and Information Fidelity." ICIP. 2014, pp. 4037–4041.
Thanks!
Muhammad Bilal on 18 Oct 2022
Thanks for your reply! Let me clarify a bit more. Matlab has at least 3 different implementations for image dehazing.
1- Function "imreducehaze" (https://www.mathworks.com/help/images/ref/imreducehaze.html)
2- Vision HDL Toolbox example (https://www.mathworks.com/help/visionhdl/ug/fog-rectification.html)
3- GPU example (https://www.mathworks.com/help/supportpkg/nvidia/ug/deploy-run-fog-rectification-video-jetson.html)
The Kaiming and Dubok references are valid for only exmple 1.
Examples 2 and 3 don't estimate Airlight at all and use quite different equations for restoring the image.
Examples 2 and 3 also differ in the use of refining filter i.e. Bilateral vs Gaussian.
Could you please provide the references for examples 2 and 3? They are interesting because they don't estimate airlight (a complex thing to do on FPGA) but the maths doesn't make sense. Thanks.
Maruthi Bhatlapenumarti on 28 Oct 2022
We have used dark channel prior for airlight estimation and bilateral filter for airlight refinement. Here is the reference:
Wei Sun, A new single-image fog removal algorithm based on physical model, Optik, Volume 124, Issue 21, 2013, Pages 4770-4775, ISSN 0030-4026.(https://www.sciencedirect.com/science/article/pii/S0030402613002866)
For contrast enhancement, you can use CLAHE, but here to keep it simple we have used basic histogram stretching. Basic contrast stretching is: https://theailearner.com/2019/01/30/contrast-stretching/
Hope that helps!

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