Optimizing Camera Placements for Overlapped Coverage with 3D Camera Projections

This paper proposes a method to compute camera 6 DoF poses to achieve a user defined coverage. The camera placement problem is modeled as a combinatorial optimization where given the maximum number of cameras, a camera set is selected from a larger pool of possible camera poses. We propose to minimize the squared error between the desired and the achieved coverage, and formulate the non-linear cost function as a mixed integer linear programming problem. A camera lens model is utilized to project the camera's view on a 3D voxel map to compute a coverage score which makes the optimization problem in real environments tractable. Experimental results in two real retail store environments demonstrate the better performance of the proposed formulation in terms of coverage and overlap for triangulation compared to existing methods.