Building tractable probabilistic graphical models for computer vision problems

Probabilistic graphical models are broadly applicable in computer vision. They can model interactions among any subset of random variables and be used to make inferences about them. However, there is a trade-off between model expressiveness and inference complexity. On one end of the spectrum, we can build models with simple graphical structures that have tractable exact inference algorithms, but their expressiveness is not strong enough to model many of the interactions in the real world. On the other end, there are models with complicated graphical structures that make the inference algorithms intractable. Thus a central theme of this dissertation is how to trade off between modeling expressiveness and inference complexity in order to achieve good model performance. We would like to model the essential interactions of random variables in graphical structures in a way that also facilitates the inference computation. For many problems such as part-based object recognition, trees are one of the candidate graphical structures due to their low inference complexity. However, they often do not have enough modeling expressiveness. We proceed to illustrate that, by applying the concepts of latent variables and hierarchical representations we can construct models with graphical structures beyond trees that capture richer interactions while still enabling efficient exact inference algorithms. For other tasks such as low-level vision problems, more expressive models with loopy graphical structures are necessary in order to properly specify the right dependence relationship among the set of random variables, even though exact inference is NP hard in this case. Approximation algorithms like Belief Propagation or Graph cuts with alpha-expansion are then applied to these models to do approximate inference. However, for loopy graphs with larger cliques there are still no good algorithms. To that end, we develop a series of approximation techniques to lower the inference complexity of Belief Propagation for these more expressive loopy graphical models and make them more effective for solving low-level vision problems. Throughout this dissertation, we investigate the trade-off between model expressiveness and inference complexity in the context of several computer vision problems, including human pose recognition from a single image, articulated object detection and tracking, and image denoising. We construct graphical models with different structural complexity for these problems, and show experimental results to evaluate and compare their performance.