Stochastic Systems Group  

Modeling and Estimating Persistent Flows with Lie Algebraic Perspective
Dahua Lin
CSAIL, MIT
In this talk, I will present a new framework in modeling persistent flows based on Lie algebra. In contrast to conventional work on motion modeling which typically aims at estimating the instantaneous velocities of individual objects, our approach tries to capture the global motion patterns that dominate a large region and persist for a long time. In doing so, we introduce the notion of geometric flow, and develop a vector space representation of the flows based on the Lie algebra of transformation groups. This representation has two advantages. First, it establishes the dual relations between trajectories and velocity fields, such that we can cast the learning of persistent motion to the problem of vector field estimation and thus eliminate the need of continuous tracking. Second, with the vector space of motion, we can decompose a complex motion into linear combination of base motions, which greatly simplifies the application of statistical learning and inference techniques. Based on this framework, we explore different ways of constructing the motion space, and develop a statistical technique that can estimate the persistent flow from noisy observations efficiently and robustly. The framework were tested on real applications including motion pattern extraction in rail station, and segmentation of natural dynamic scenes.
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