Abstract: Robust human pose estimation is a challenging problem in computer vision in that body part configurations are often subject to severe deformations and occlusions. Moreover, efﬁcient pose estimation is often a desirable requirement in many applications. The trade-off between accuracy and efﬁciency has been explored in a large number of approaches. On the one hand, models with simple representations (like tree or star models) can be efﬁciently applied in pose estimation problems. However, these models are often prone to body part misclassification errors. On the other hand, models with rich representations (i.e., loopy graphical models) are theoretically more robust, but their inference complexity may increase dramatically. In this talk, we present an efﬁcient and exact inference algorithm based on branch-and-bound to solve the human pose estimation problem on loopy graphical models. We show that our method is empirically much faster (about 74 times) than the state-of-the-art exact inference algorithm [Sontag et al. UAI’08]. By extending a state-of-the-art tree model [Sapp et al. ECCV’10] to a loopy graphical model, we show that the estimation accuracy improves for most of the body parts (especially lower arms) on popular datasets such as Buffy [Ferrari et al. CVPR’08] and Stickmen [Eichner and Ferrari BMVC’09] datasets. Our method can also be used to exactly solve most of the inference problems of Stretchable Models [Sapp et al. CVPR’11] on video sequences (which contains a few hundreds of variables) in just a few minutes. Finally, we show that the novel inference algorithm can potentially be used to solve human behavior understanding and biological computation problems.