Optimal Camera Placement to measure Distances Conservativly Regarding Static and Dynamic Obstacles

In modern production facilities industrial robots and humans are supposed to interact sharing a common working area. In order to avoid collisions, the distances between objects need to be measured conservatively which can be done by a camera network. To estimate the acquired distance, unmodelled objects, e.g., an interacting human, need to be modelled and distinguished from premodelled objects like workbenches or robots by image processing such as the background subtraction method. The quality of such an approach massively depends on the settings of the camera network, that is the positions and orientations of the individual cameras. Of particular interest in this context is the minimization of the error of the distance using the objects modelled by the background subtraction method instead of the real objects. Here, we show how this minimization can be formulated as an abstract optimization problem. Moreover, we state various aspects on the implementation as well as reasons for the selection of a suitable optimization method, analyze the complexity of the proposed method and present a basic version used for extensive experiments.