We study the geometry and kinematics of surveillance of static objects with moving cameras both in 2D and 3D space via geometric algebras. The former case is easily handled using polar representation of complex numbers, while for the latter we resort on dual projective quaternions and Pl\"{u}cker line geometry. Hence, a brief preliminary section is provided, after which we approach the task naively, searching for exact solutions in the case of pre-determined trajectory. The infinitesimal setting is of particular interest for practical reasons, so we pay attention to it as well. Finally, some ideas for generalizations are given, along with curious examples.