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Senjian An, Patrick Peursum, Wanquan Liu, Svetha Venkatesh, and Xaoiming Chen. Exploiting monge structures in optimum subwindow search. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE CS Press, 2010.

Optimum subwindow search for object detection or image part retrieval aims to find a subwindow of the image so that the subimage is most similar to the object in query. We will formulate it as a four dimensional (4D) combinatorial optimization problem. A naive exhaustive search requires O(n4) sequential computations for n x n images. However, for some typical similarity functions like Euclian metric, X2 metric on image histograms, the associated 4D array carries some Monge structures which can be used to speed up the optimum subwindow search. By exploiting the Monge structures, we will propose an alternating column and row search method with typical quadratic time complexity O(n2). Experiments on PASCAL VOC 2006 demonstrate that the alternating method is significantly faster than the well known efficient subwindow search (ESS) method

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