1. A method for detecting loitering behavior of objects depicted in a scene captured by a video camera, the method comprising: receiving a trajectory for an object in the scene, wherein the object has been in the scene for a time period, and wherein the trajectory tracks a two-dimensional (2D) path of the object relative to a series of video frames in which the object is depicted; and upon determining that the time period that the object has been in the scene is greater than a threshold time period and determining that the trajectory corresponds to a random walk, generating a loitering alert.