One of the goals of a multi-camera surveillance system is to collect useful video clips of objects in the scene. Objects in the collected videos should be unobstructed, in the field of view of the given camera, and meet task-specific resolution requirement. For this purpose, we describe an algorithm that constructs "task visibility intervals", which are tuples of information about what to sense (task-object pairs), when to sense (feasible future temporal intervals to start a task) and how to sense (the camera to use and the corresponding viewing angles and focal length). The algorithm first looks for temporal intervals within which the angular extents of objects overlap each other, causing the object farthest from the given camera to be occluded. Outside these intervals, sub-intervals are then constructed such that feasible camera settings exist for capturing the object. Experimental results are provided to illustrate the system capabilities in constructing such task visibility intervals, followed by scheduling them using a greedy algorithm.