We address the problem of surveillance in an environment with obstacles. We show that the problem of tracking an evader with one pursuer around one corner is completely decidable. The pursuer and the evader have complete information about each other's instantaneous position. The pursuer has complete information about the instantaneous velocity of the evader. We present a partition of the visibility region of the pursuer where based on the region in which the evader lies, we provide strategies for the evader to escape the visibility region of the pursuer or for the pursuer to track the target for all future time. We also present the solution to the inverse problem: given the position of the evader, the positions of the pursuer for which the evader can escape the visibility region of the target. These results have been provided for varying speeds of the pursuer and the evader. Based on the results of the inverse problem we provide an O(n3 log n) algorithm that can decide if the evader can escape from the visibility region of a pursuer for some initial pursuer and evader positions. Finally, we extend the result of the target tracking problem around a corner in two dimensions to an edge in three dimensions.