Optimization for 3D Model-based Multi-Camera Deployment

Abstract

Based on convex optimization techniques, we propose a new multi-camera deployment method for optimal visual coverage of a three-dimensional (3D) object surface. Different from existing methods, the optimal placement of a single camera is formulated as two convex optimization problems, given a set of covered triangle faces. Moreover, this idea is incorporated into a recursive framework to expand the covered area for each camera, wherein initially covered triangle faces are elegantly chosen using an importance criterion for the first recursion. By placing cameras one by one using the same method, the object surface is gradually covered by iteratively removing the covered partition of the previously deployed camera. Due to the usage of convex optimization, each camera is guaranteed to be placed at an optimal pose for a group of triangle faces other than a single one. This merit, together with the importance criterion-based selection of initially covered triangle faces, reduces the number of required cameras while satisfying various constraints including the resolution, field of view, focus and occlusion. Simulation results on two real 3D computer-aided design (CAD) models are presented to verify the effectiveness of the proposed approach.