Camera setup optimization for optical tracking in virtual environments

In this paper we present a method for finding the optimal camera alignment for a tracking system with multiple cameras, by specifying the volume that should be tracked and an initial camera setup. The approach we use is twofold: on the one hand, we use a rather simple gradient based steepest descent method and on the other hand, we also implement a simulated annealing algorithm that features guaranteed optimality assertions. Both approaches are fully automatic and take advantage of modern graphics hardware since we implemented a GPU-based accelerated visibility test. The proposed algorithms can automatically optimize the whole camera setup by adjusting the given set of parameters. The optimization may have different goals depending on the desired application, e.g. one may wish to optimize towards the widest possible coverage of the specified volume, while others would prefer to maximize the number of cameras seeing a certain area to overcome heavy occlusion problems during the tracking process. Our approach also considers parameter constraints that the user may specify according to the local environment where the cameras have to be set up. This makes it possible to simply formulate higher level constraints e.g. all cameras have a vertical up vector. It individually adapts the optimization to the given situation and also asserts the feasibility of the algorithm's output.