Optimal camera placement to obtain accurate 3D point positions

The problem we would like to approach is the automation of the camera network design process in order to obtain accurate 3D measurements. We restrict ourselves to the problem where the camera positions are limited only by the incidence angle constraint and it is simplified to the case where the cameras remain at a fixed distance to the set of target points to be measured. The main question we would like to answer is: Where should we place the cameras in order to obtain the minimal 3D error? From this question several subproblems arise; How can we develop a good criterion to judge our configuration? What conditions are needed for our system to work? Which are the interrelated aspects involved in the development of the system? What would be a good method to optimize the placement of the camera? From these initial questions the choice of a criterion combined with an optimization process will be the key concepts. Researchers in the computer vision and photogrammetric communities have recognized the need to automate the process of camera network design. Tarbox and Gottschlich [7] have recognised the need for multistation solutions to overcome object occlusion problems. They have implemented a solution in the IVIS system for an active triangulation sensor. Fritsch and Crosilla [3] have investigated the potential of optimizing multi-station configurations using an analytical first order design (FOD) approach by iteratively shifting the sensor stations until the covariance matrix of the estimated object feature coordinates is better than a criterion matrix. However their approach is limited to the optimization of existing configurations. A work called CONSENS which follows the expert system approach and uses multiple cameras in combination with optical triangulation, was developed by Mason et al. [5]. It describes an ideal configuration of four camera stations that can be employed to provide a strong imaging geometry for the class of planar network design problems. Complex objects are di-