With rapid profusion of video data, automated surveillance and intrusion detection is becoming closer to reality. In order to provide timely responses while limiting false alarms, an intrusion detection system must balance resources (e.g., time) and accuracy. In this paper, we show how such a system can be modeled with a partially observable Markov decision process (POMDP), representing possible computer vision filters and their costs in a way that is similar to human vision systems. The POMDP representation can be optimized to produce a dynamic sequence of operations and achieve a trade-off between time and detection quality, taking into account uncertainty in the filter predictions. In a set of experiments on actual video data, we show that our method can both outperform static "expert" models and scale to large dynamic domains. These results suggest that our method could be used in real-world intrusion detection systems.