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We introduce a general approach for surveillance of robots using depth images of multiple distributed smart cameras which can be either standard colour cameras or depth cameras. Unknown objects intruding the robot workcell are detected in the camera images and the minimum distance between the robot and all these detected unknown objects is calculated. The surveillance system is built as master-slave architecture with one slave per distributed camera. The level of distributed processing on the slaves (from pure image acquisition up to minimum distance calculation) controls the remaining computations on the master and thus the quality of approximation of the detected unknown objects. The calculated minimum distance and the asymptotic overall surveillance cycle time are evaluated in experiments.