Inference in Large-Scale Graphical Models and its application to SFM, SAM, and SLAM
Simultaneous Localization and Mapping (SLAM), Smoothing and Mapping (SAM), and Structure from Motion (SFM) are important and closely related problems in robotics and vision. Not surprisingly, there is a large literature describing solutions to each problem, and more and more connections are established between the two fields. At the same time, robotics and vision researchers alike are becoming increasingly familiar with the power of graphical models as a language in which to represent inference problems. In this talk I will show how SFM, SAM, and SLAM can be posed in terms of this graphical model language, and how inference in them can be explained in a purely graphical manner via the concept of variable elimination. I will then present a new way of looking at inference that is equivalent to the junction tree algorithm yet is - in my view- much more insightful. I will also show that, when applied to linear(ized) Gaussian problems, the algorithm yields the familiar QR and Cholesky factorization algorithms, and that this connection with linear algebra leads to strategies for very fast inference in arbitrary graphs. I will conclude by showing some published and preliminary work that exploits this connection to the fullest.