在惡劣天氣條件下的能見度極差是因為大氣懸浮粒子所造成的，例如：大霧
或水氣。「還原一張受上述大氣影響的模糊影像」這類問題通常簡稱為「去霧」。單張影像去霧所面臨的挑戰主要來自於兩項未知:場景深度以及場景原始色彩。其中光線傳播率圖包含了場景深度的資訊，求得光線傳播率圖的近似值便是解決去霧問題中最關鍵的步驟。在本論文中，我們假設光線傳播率圖具有特定的趨勢，並依據此假設將去霧模型推導出具最佳傳播率圖之解的式子。我們所推導的目標函數保證有全域最佳解，因此得到的光線傳播率圖相當準確，並且同一物體的深度具有一致性。最後，我們考慮到光在三個色彩通道上因波長不同而導致傳播率有所差異。利用最佳光線傳播率圖、並考慮每個色彩通道上具備不同波長的特性，我們的方法能夠成功的去除掉影像中的霧靄影響，得到相當優異的影像。

The poor visibility in bad weather condition, such as haze and fog, is caused by the stationary atmospheric effects of suspended particles. The challenge of restoring such atmospheric effects, usually referred to as “dehazing”, from single image mainly comes from the double uncertainty of scene depth and scene radiance. Approximation of the transmission, which encodes the scene depth information, is the most significant step to solve the dehazing problem. In this thesis, we propose to derive an optimal transmission map under a heuristic assumption in the dehazing model. The proposed objective function guarantees to have a global optimal solution, and the obtained transmission map is accurate and preserves the depth-consistency of the same object. Finally, we further take the difference in light wavelengths transmission between three color channels into account. Using the optimal transmission map and considering the different wavelengths of each color channel, our method recovers haze-free images with excellent result.

[1] S. Shwartz, E. Namer, and Y.Y. Schechner, “Blind Haze Separation,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 1984–1991, 2006.
[2] S.G. Narasimhan and S.K. Nayar, “Contrast Restoration of Weather Degraded Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 6 pp. 713–724, June 2003.
[3] S.G. Narasimhan and S.K. Nayar, “Interactive Deweathering of an Image Using Physical Models,” Proc. IEEE Workshop on Color and Photometric Methods in Computer Vision, pp. 1387–1394, Oct. 2003.
[4] J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: Model-Based Photograph Enhancement and Viewing,” ACM Trans. Graphics, vol. 27, no. 5, pp.116:1–116:10, 2008.
[5] R. Fattal, “Single Image Dehazing,” ACM Trans. on Graphics, 2008.
[6] J. Tarel and N. Hautiere, “Fast Visibility Restoration from A Single Color or Gray Level Image,” Proc. IEEE Conf. Computer Vision, pp. 2201–2208, 2009.
[7] R. Tan, “Visibility in Bad Weather from a Single Image,” IEEE Conf. Computer Vision and Pattern Recognition, pp.1–8, June 2008.
[8] K. He, J. Sun and X. Tang, “Single Image Haze Removal Using Dark Channel Prior,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol.33, No.12, pp.2341–2353, Aug. 2010.
[9] K. Nishino, L. Kratz and S. Lombardi, “Bayesian Defogging,” International Journal of Computer Vision, pp.1–16, 2011.
[10] A. Levin, D. Lischinski and Y. Weiss, “A Closed Form Solution to Natural Image Matting,” Proc. IEEE Conf. on Computer Vision and Pattern Recognition, vol. 1, pp. 61–68, June 2006.
[11] S. Paris and F. Durand, “A Fast Approximation of the Bilateral Filter using a Signal Processing Approach,” Proc. European Conf. Computer Vision, pp. 568–580, 2006.
[12] Y.Y. Schechner, S.G. Narasimhan, and S.K. Nayar, “Instant Dehazing of Images Using Polarization,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 325-332, 2001.
[13] J. Chiang and Y. Chen, “Underwater Image Enhancement by Wavelength Compensation and Dehazing,” IEEE Trans. Image Processing, Vol. 21, No. 4, April 2012.
[14] S. Q. Duntley, “Light in the sea,” J. Opt. Soc. Amer., vol. 53, no. 2, pp.214–233, 1963.
[15] L. Chao and M. Wang, “Removal of Water Scattering,” Proc. IEEE International Conference on Computer Engineering and Technology (ICCET), vol. 2, pp. 35–39, 2010.
[16] S. Narasimhan, S. Nayar, “Chromatic Framework for Vision in Bad Weather, ” IEEE Conference on Computer Vision and Pattern Recognition, 2000.
[17] S. Paris and F. Durand, “A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach,” Proc. European Conf. Computer Vision, pp. 568–580, 2006.