Efficient Global Optimization of Non-Differentiable, Symmetric Objectives for Multi Camera Placement

We propose a novel iterative method for optimally placing and orienting multiple cameras in a 3D scene. Sample applications include improving the accuracy of 3D reconstruction, maximizing the covered area for surveillance, or improving the coverage in multi-viewpoint pedestrian tracking. Our algorithm is based on a block-coordinate ascent combined with a surrogate function and an exclusion area technique. This allows to flexibly handle difficult objective functions that are often expensive and quantized or non-differentiable. The solver is globally convergent and easily parallelizable. We show how to accelerate the optimization by exploiting special properties of the objective function, such as symmetry. Additionally, we discuss the trade-off between non-optimal stationary points and the cost reduction when optimizing the viewpoints consecutively.