@conference {14848,
	title = {Approximate earth mover{\textquoteright}s distance in linear time},
	booktitle = {Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on},
	year = {2008},
	month = {2008/06//},
	pages = {1 - 8},
	abstract = {The earth moverpsilas distance (EMD) is an important perceptually meaningful metric for comparing histograms, but it suffers from high (O(N<sup>3</sup> logN)) computational complexity. We present a novel linear time algorithm for approximating the EMD for low dimensional histograms using the sum of absolute values of the weighted wavelet coefficients of the difference histogram. EMD computation is a special case of the Kantorovich-Rubinstein transshipment problem, and we exploit the Holder continuity constraint in its dual form to convert it into a simple optimization problem with an explicit solution in the wavelet domain. We prove that the resulting wavelet EMD metric is equivalent to EMD, i.e. the ratio of the two is bounded. We also provide estimates for the bounds. The weighted wavelet transform can be computed in time linear in the number of histogram bins, while the comparison is about as fast as for normal Euclidean distance or chi<sup>2</sup> statistic. We experimentally show that wavelet EMD is a good approximation to EMD, has similar performance, but requires much less computation.},
	keywords = {algorithm;normal, complexity;earth, complexity;image, constraint;Kantorovich-Rubinstein, continuity, distance;histograms;linear, distance;weighted, Euclidean, Holder, matching;wavelet, movers, problem;computational, TIME, transform;computational, transforms;, transshipment, wavelet},
	doi = {10.1109/CVPR.2008.4587662},
	author = {Shirdhonkar,S. and Jacobs, David W.}
}
@conference {14841,
	title = {3-D to 2-D recognition with regions},
	booktitle = {Computer Vision and Pattern Recognition, 1997. Proceedings., 1997 IEEE Computer Society Conference on},
	year = {1997},
	month = {1997/06//},
	pages = {547 - 553},
	abstract = {This paper presents a novel approach to parts-based object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3-D object from a single 2-D image when convex parts of the object have been matched to corresponding regions in the image. We consider three types of occlusions: self-occlusion, occlusions whose locus is identified in the image, and completely arbitrary occlusions. We derive efficient algorithms for the first two cases, and characterize their performance. For the last case, we prove that the problem of finding valid poses is computationally hard, but provide an efficient, approximate algorithm. This work generalizes our previous work on region-based object recognition, which focused on the case of planar models},
	keywords = {2-D, algorithms;object, complexity;image, hard;efficient, image;3-D, object;computationally, poses;computational, recognition;, recognition;occlusion;occlusions;performance;regions;valid, segmentation;object},
	doi = {10.1109/CVPR.1997.609379},
	author = {Jacobs, David W. and Basri,R.}
}
