Continuous sensing of the environment from a mobile robot perspective can prevent harmful collisions between human and mobile service robots. However, the overall collision avoidance performance depends strongly on the optimal placement of multiple depth sensors on the mobile robot and maintains flexibility of the working area. In this paper, we present a novel approach to optimal sensor placement based on the visibility of the human in the robot environment combined with a quantified risk of collision. Human visibility is determined by ray tracing from all possible camera positions on the robot surface, quantifying safety based on the speed and direction of the robot throughout a pre-determined task. A cost function based on discrete cells is formulated and solved numerically for two scenarios of increasing complexity, using a CUDA implementation to reduce computation time.