超解析度方法是影像處理領域中的一種基礎操作，涉及如何提高一張影像的解析度而不過度損害其影像品質。近年有多項研究致力於發展基於像素或基於區塊的高性能超解析度方法。這樣的方法對老照片或經典電影等低解析度內容的再利用相當重要。本論文提出一種使用雙邊濾波框架但採用特殊濾波器的新型超解析度方法。給定一張低解析度影像，我們首先收集所需的兩種濾波器。第一種由Jinc函數在空間域中定義，而另一種則由演化式賽局在特徵域中決定。Jinc函數所定義的濾波器十分優異但濾波後只能保存空間域中的相似性。而特徵域中的演化式賽局藉由將每一個未知的高解析度像素視為一個玩家，進一步達到一種演化平衡狀態，因此決定出的濾波器能保存特徵域中的相似性。我們結合這兩種濾波器以對給定的低解析度影像進行雙邊濾波處理，並取得它的放大版本作為結果。實驗結果展示了所提出的方法能保持比常見方法更高的峰值訊噪比，同時移除大部分的振鈴效應。做為未來的研究方向，結合人類視覺與電腦視覺以創建一種兼具主觀與客觀的新衡量標準是值得深入研究的。

Super resolution is a basic operation in image processing, involving how to increase resolution of an image with minimum damage to its visual quality. A great deal of work has been done recently on developing super resolution methods for better performance for either pixel-based or patch-based. Such methods are essential for reusing low-resolution contents like old low-resolution pictures or classical movies. This paper proposes a new super resolution method, using the framework of bilateral filtering but adopting special filters instead. Given a low-resolution image, we first gather two kind of required filters. The first kind is Jinc filter defined by the Jinc function in spatial domain, and the other kind is Game filter determined by an evolutionary game in feature domain. Jinc filter is powerful but preserves only spatial similarity when used in filtering. By regarding each unknown high-resolution pixel as a player, the evolutionary game in feature domain further achieves an evolutionary convergent state to obtain the Game filter, hence preserves feature similarity. Combining these two kind of filters, we then perform the bilateral filtering process over the low-resolution image to obtain its enlarged version as result. Experimental results show that the proposed method could keep higher PSNR value than common methods while getting rid of most ringing effect. As the future work, an interesting direction to explore is creating a new measurement, which is both subjective and objective, by mixing human vision and computer vision.

[1] R. Keys, "Cubic convolution interpolation for digital image processing," IEEE TranS. Acoust., Speech, Signal Process., vol. 29, no. 6, pp. 1153-1160, Dec. 1981.
[2] W. T. Freeman, T. R. Jones and E. C. Pasztor, "Example-Based Super-Resolution," IEEE Computer Graphics and Applications, vol. 22, no. 2, pp. 56-65, 2002.
[3] J. Yang, J. Wright, T. S. Huang and Y. Ma, "Image super-resolution as sparse representation of raw image patches," in CVPR, 2008.
[4] D. Glasner, S. Bagon and M. Irani, "Super-resolution from a single image," in ICCV, 2009.
[5] G. Freedman and R. Fattal, "Image and video upscaling from local self-examples," ACM Trans. Graph., vol. 30, no. 2, p. 12, April 2011.
[6] W. Dong, L. Zhang, G. Shi and X. Wu, "Nonlocal back-projection for adaptive image enlargement," in ICIP, 2009.
[7] M. Irani and S. Peleg, "Motion Analysis for Image Enhancement: Resolution, Occlusion, and Transparency," JVCIR, vol. 4, no. 4, pp. 324-335, Dec. 1993.
[8] S. Dai, M. Han, Y. Wu and Y. Gong, "Bilateral Back-Projection for Single Image Super Resolution," in ICME, 2007.
[9] Q. Shan, Z. Li, J. Jia and C.-K. Tang, "Fast image/video upsampling," ACM Trans. Graph., vol. 27, no. 5, p. 153, 2008.
[10] P. Getreuer, "Linear Methods for Image Interpolation," Image Processing On Line, vol. 2011, 2011.
[11] A. Aldroubi, M. Unser and M. Eden, "Cardinal spline filters: Stability and convergence to the ideal sinc interpolator," Signal Processing, vol. 28, no. 2, pp. 127-138, Aug. 1992.
[12] M. Unser, "Splines: a perfect fit for signal and image processing," IEEE Signal Processing Magazine, vol. 16, no. 6, pp. 22-38, Nov. 1999.
[13] Y. Chen, Y. Gao and K. J. R. Liu, "An evolutionary game-theoretic approach for image interpolation," in ICASSP, 2011.
[14] M. Smith, Evolution and the Theory of Games, Cambridge University Press, 1982.
[15] J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988.
[16] W. R. Hendee and P. N. T. Wells, The Perception of Visual Information, Springer Verlag, 1997, p. 204.
[17] C. Tomasi and R. Manduchi, "Bilateral Filtering for Gray and Color Images," in ICCV, 1998.