Background Extraction常常運用在電腦影像視覺上，例如：物件追蹤和偵測。
而通常這些方法都是假定已經有一張乾淨的背景存在以供使用，
但是現實生活上，有很多情況是沒辦法直接取得一乾淨的背景。
本論文提出了一個利用Random Walk Model觀念來作Background Extraction的方法。
首先將影片中的所有frame經過前處理後，取得``無動量背景"，
接著制定兩個衡量準則來判斷像素的對比度和空間上的關係，並且以此為取捨背景像素的依據。
利用無動量背景和這兩個衡量準則來當作Random Walk的輸入，
計算並取得每一``無動量背景"所對應到的權重矩陣，進而將影像融合取得乾淨的背景結果。
實驗結果證明，本方法與現今最新的方法比較，可以更漂亮的擷取出乾淨的背景。

Background extraction is important for various applications, such as object tracking and detection. In this work, we propose a background extraction algorithm with a stochastic model based on the theory of random walks.We first utilize optical flow technique to obtain no-motion backgrounds from all input frames. We then formulate the background extraction problem as a probability estimation problem. The resultant background is obtained by solving the optimal solution of the probability estimation problem. Experimental results show that the proposed algorithm outperforms many state-of-the-art techniques in visual quality.

[1] A. Colombari and A. Fusiello, "Patch-based background initialization in heavily
cluttered video," IEEE Transactions on Image Processing, vol. 19, pp. 926-933,
Apr. 2010.
[2] R. Kapoor and A. Dhamija, "Fast tracking algorithm using modi ed potential
function," Computer Vision, IET, vol. 6, pp. 111-120, Mar. 2012.
[3] D.-M. Tsai and S.-C. Lai, "Independent component analysis-based background
subtraction for indoor surveillance," IEEE Transactions on Image Processing,
vol. 18, pp. 158{167, Jan. 2009.
[4] R. Marie, A. Potelle, and E. Mouaddib, "Dynamic background subtraction us-
ing moments," IEEE International Conference on Image Processing, pp. 2369-
2372, Sept. 2011.
[5] O. Barnich and M. Van Droogenbroeck, "Vibe: A universal background sub-
traction algorithm for video sequences," IEEE Transactions on Image Process-
ing, pp. 1709-1724, June. 2011.
[6] K. Toyama, J. Krumm, B. Brumitt, and B. Meyers, "Wall
ower: Principles
and practice of background maintenance," IEEE International Conference on
Computer Vision, vol. 1, pp. 255-261, 1999.
[7] W. Long and Y. Yang, "Stationary background generation: an alternative to
the di erence of two images," Pattern Recognition, vol. 23, pp. 1351-1359, 1990.
[8] V. Reddy, C. Sanderson, and B. Lovell, "An e cient and robust sequential
algorithm for background estimation in video surveillance," IEEE International
Conference on Image Processing, pp. 1109-1112, 2009.
[9] V. Reddy, C. Sanderson, and B. Lovell, "A low-complexity algorithm for static
background estimation from cluttered image sequences in surveillance con-
texts," Journal on Image and Video Processing, Apr. 2011.
[10] C.-C. Chen and J. K. Aggarwal, "An adaptive background model initializa-
tion algorithm with objects moving at di erent depths," IEEE International
Conference on Image Processing, 2008.
[11] S. Kakutani, "Markov processes and the dirichlet problem," Proc. Japanese
Academy, vol. 21, pp. 227-233, 1945.
[12] P. Doyle and L. Snell, "Random walks and electric networks," Washington,
D.C.: Mathematical Association of America, 1984.
[13] R.Courant and D. Hilbert, "Methods of math. physics," John Wiley and Sons,
1989.
[14] R. Hersh and R. Griego, "Brownian motion and potential theory," Scienti c
American, vol. 220, pp. 67-74, 1969.
[15] H. Wechsler and M. Kidode, "A random walk procedure for texture discrim-
ination," IEEE Transactions on Pattern Analysis and Machine Intelligence,
vol. PAMI-1, pp. 271-280, 1979.
[16] N. Biggs, "Algebraic potential theory on graphs," Bull. London Mathematical
Society., pp. 641-682, 1997.
[17] L. Grady, "Random walks for image segmentation," IEEE Transactions on
Pattern Analysis and Machine Intelligence, vol. 28, pp. 1768-1783, Nov. 2006.
[18] R. Shen, I. Cheng, J. Shi, and A. Basu, "Generalized random walks for fusion
of multi-exposure images," IEEE Transactions on Image Processing, vol. 20,
pp. 3634-3646, Dec. 2011.
[19] B. Lucas and T. Kanade, "An iterative image registration technique with an
application to stereo vision," International Joint Conferences on Arti cial In-
telligence(IJCAI), pp. 674-679, 1981.
[20] S. Baker and I. Matthews, "Lucas-kanade 20 years on: A unifying framework,"
International Journal of Computer Vision(IJCV), pp. 221-255, 2004.
[21] D. Gutchess, M. Trajkovics, E. Cohen-Solal, D. Lyons, and A. Jain, "A back-
ground model initialization algorithm for video surveillance," IEEE Interna-
tional Conference on Computer Vision, vol. 1, pp. 733-740, Nov. 2001.
[22] F. Chung, "Spectral graph theory," Providence, R.I.: American Mathematical
Society, 1997.
[23] N. Biggs, "Algebraic graph theory," Cambridge University Press, 1974.
[24] D. Marr and E. Hildreth, "Theory of edge detection," Proc. of the Royal Society,
pp. 187-217, 1980.
[25] T. Mertens, J. Kautz, and F. V. Reeth, "Exposure fusion," Computer Graphics
and Applications, pp. 382-390, 2007.