Bayesian discounting of camera parameter uncertainty for optimal 3D reconstruction from images

3D reconstruction through point correspondences is a process that is sensitive to match errors and also to possible ambiguity in the solution space of shape and camera estimates - the existence of either or the combination of both propagates into sub-optimal estimates of the structure. To counteract this, most methods in the field jointly or sequentially estimate both the camera parameters and the 3D structure using methods such as Bundle Adjustment. However, joint estimation methods such as Bundle Adjustment find sub-optimal solutions of structure if the structure is not uniquely defined in the joint space. Using probabilistic models for reconstruction and marginalizing across camera parameter uncertainty we show how to compute the optimal 3D reconstruction. We use only uniform priors to make comparisons between Bundle Adjustment and our work. However, the method, by its construction, is set up to use prior information about either the camera parameters or the 3D structure, if it is available. Results show that this method produces better reconstruction estimates than joint estimation methods such as Bundle Adjustment especially in the face of increasing noise in the feature correspondences.