Optimum Fiducials under Weak Perspective Projection

We investigate how a given fixed number of points should be located in space so that the pose of a camera viewing them from unknown locations can be estimated with the greatest accuracy. We show that optimum solutions are obtained when the points form concentric complete regular polyhedra. For the case of optimal configurations we provide a worst-case error analysis and use it to analyze the effects of weak perspective approximation to true perspective viewing. Comprehensive computer simulations validate the theoretical results.