影像共分割是電腦視覺領域中的新興議題，近年來在許多文獻中被熱烈討論著。其主要目的是從一組輸入的影像中，分割出它們所共同具有的區域或物件。由於過去的方法存在一些限制，在本篇論文中我們利用熱源擴散以及顯著性的概念，提出一個基於合作賽局的非監督式影像共分割方法，目的是要排除這些限制並達到高準確率。此方法大致上可分為兩個階段：首先，我們提出一個合作賽局模型來找出影像中的共同物件，在這個合作賽局中，我們將每張影像視為個別的玩家，所有玩家企圖透過放置熱源在系統中以獲得總體的最大熱能提升。
為了保證玩家總是採取合作行為，我們定義了一些協同策略，使得玩家在選取熱源的時候，必須考慮到與其他玩家的相似度，且所選取的熱源須具有較高的顯著值。透過適當的賽局定義，來讓這些影像一同找出它們所共同具有的物件。此賽局架構會針對每張影像產生出對應的標記影像，分別指出那些確定為共同物件以及背景的部分。在第二階段我們應用Cooperative cut的方法來解決能量最小化問題並產生分割結果。本篇論文所提出的方法充分運用了合作賽局的概念，讓我們能夠自動化並準確地找出各影像所共同具有的物件，實驗結果顯示所提出的方法在各種不同情況下，皆優於現有的影像共分割方法。

Co-segmentation is a new topic in computer vision, which has been discussed lively in many literatures. It is defined as the task of jointly segmenting the common objects in a given set of images. Due to there are some limitations in previous methods, this thesis presents a game theoretic unsupervised approach by using the concept of heat diffusion and saliency to solve co-segmentation problem without these limitations. Our method is divided into two stages. First, the common objects discovery task is modeled by a cooperative game. In this game, each image is treated as player. All players want to maximize the overall payoffs (i.e. the gain of heat) by putting the heat sources appropriately. Note that we must ensure that no one will be likely to uncooperative. So we define some collaborative strategies.
For each input image, the game structure generates corresponding labeled image which identifies the common objects and background. Then we use cooperative cut to solve energy minimization problem in the second stage. Our method takes advantage of cooperative game theory, which enables us to discover the common objects automatically and accurately. Experimental results demonstrate that in many cases the proposed method can perform much better than state-of-the-art co-segmentation method.

[1] C. Rother, T. Minka, A. Blake, and V. Kolmogorov. Cosegmentation of Image Pairs by Histogram Matching Incorporating a Global Constraint into MRFs. In CVPR, 2006.
[2] L. Mukherjee, V. Singh, and C. R. Dyer. Half-integrality based algorithms for cosegmentation of images. In CVPR, 2009.
[3] D. S. Hochbaum and V. Singh. An Efficient Algorithm for Cosegmentation. In ICCV, 2009.
[4] S. Vicente, V. Kolmogorov, C. Rother, "Cosegmentation Revisited: Models and Optinization,” Proc. European Conference on Computer Vision, pp. 465-479, 2010.
[5] Y.Y. Boykov, and M.P. Jolly, "Interactive Graph Cuts for Optimal Boundary and Region Segmentation of Objects in N-D images,” IEEE Int’l Conf. Computer Vision, pp. 105-112, 2001.
[6] A. Joulin, F. Bach, and J. Ponce. Discriminative Clustering for Image co-segmentation. In CVPR, 2010.
[7] G. Kim, E. P. Xing, L. Fei-Fei, and T. Kanade, Distributed Cosegmentation via Submodular Optimization on Anisotropic Diffusion, 13th International Conference on Computer Vision. (ICCV 2011), Spain, 2011.
[8] W. S. Chu, C. P. Chen, and C. S. Chen. MOMI-cosegmentation: Simultaneous segmentation of multiple objects among multiple images. In Asian Conf. on Comp. Vision, 2010.
[9] D. Batra, A. Kowdle, D. Parikh, J. Luo, and T. Chen. iCoseg: Interactive Co-segmentation with Intelligent Scribble Guidance. In CVPR, 2010.
[10] D. Batra, A. Kowdle, D. Parikh, J. Luo, and T. Chen. Interactively co-segmentating topically related images with intelligent scribble guidance. International Journal of Computer Vision, To Appear, 2011.
[11] J. Cui, Q. Yang, F. Wen, Q. Wu, C. Zhang, L. V. Gool, and X. Tang. Transductive object cutout. In CVPR, 2008.
[12] J. Zhang, J. Zheng, and J. Cai. A Diffusion Approach to Seeded Image Segmentation. In CVPR, 2010.
[13] J. Weickert. Anisotropic Diffusion in Image Processing. ECMI Series, Teubner-Verlag, 1998.
[14] A. Bruhn, J. Weickert, and C. Schn¨orr. Lucas/Kanade Meets Horn/Schunck: Combining Local and Global Optic Flow Methods. IJCV, 61(3):211–231, 2005.
[15] J. Harel, C. Koch, and P. Perona, "Graph-Based Visual Saliency", Proceedings of Neural Information Processing Systems (NIPS), 2006.
[16] S. Jegelka and J. Bilmes. Submodularity beyond submodular energies: coupling edges in graph cuts, CVPR 2011.
[17] A. Levinshtein, A. Stere, K. Kutulakos, D. Fleet, S. Dickinson, and K. Siddiqi. TurboPixels: Fast Superpixels Using Geometric Flows. IEEE PAMI, 31(12):2290–2297, 2009.
[18] G. Mori, Guiding Model Search Using Segmentation, IEEE International Conference on Computer Vision, 2005.
[19] L. Vincent and P. Soille, Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations. PAMI, 13(6):583–598, 1991.
[20] C. Rother, V. Kolmogorov, and A. Blake. Grabcut – interactive foreground extraction using iterated graph cuts. In SIGGRAPH, 2004.
[21] S. Vicente, V. Kolmogorov, and C. Rother. Graph cut based image segmentation with connectivity priors. In CVPR, 2008.
[22] D. Freedman and P. Drineas. Energy minimization via graph cuts: Settling what is possible. In CVPR, 2005.
[23] V. Kolmogorov and R. Zabih. What energy functions can be minimized via graph cuts? IEEE TPAMI, 26(2):147–159, 2004.
[24] Y. Boykov and V. Kolmogorov, “An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124-1137, Sept. 2004.
[25] J. Winn, A. Criminisi, and T. Minka. Object Categorization by Learned Universal Visual Dictionary. In ICCV, 2005.
[26] J. Deng,W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei. ImageNet: A Large-Scale Hierarchical Image Database. In CVPR, 2009.