Fast Exact Hyper-graph Matching with Dynamic Programming for Spatio-temporal Data

Graphs and hyper-graphs are frequently used to recognize complex and often non-rigid patterns in computer vision, either through graph matching or point-set matching with graphs. Most formulations resort to the minimization of a difficult energy function containing geometric or structural terms, frequently coupled with data attached terms involving appearance information. Traditional methods solve the minimization problem approximately, for instance resorting to spectral techniques. In this paper, we deal with the spatio-temporal data, for a concrete example, human actions in video sequences. In this context, we first make three realistic assumptions: (i) causality of human movements; (ii) sequential nature of human movements; and (iii) one-to-one mapping of time instants. We show that, under these assumptions, the correspondence problem can be decomposed into a set of subproblems such that each subproblem can be solved recursively in terms of the others, and hence an efficient exact minimization algorithm can be derived using dynamic programming approach. Secondly, we propose a special graphical structure which is elongated in time. We argue that, instead of approximately solving the original problem, a solution can be obtained by exactly solving an approximated problem. An exact minimization algorithm is derived for this structure and successfully applied to action recognition in two settings: video data and Kinect coordinate data.