Efficiently Determining Silhouette Consistency

Volume intersection is a frequently used technique to solve the Shape-From-Silhouette problem, which constructs a 3D object estimate from a set of silhouettes taken with calibrated cameras. It is natural to develop an efficient algorithm to determine the consistency of a set of silhouettes before performing time-consuming reconstruction, so that inaccurate silhouettes can be omitted. In this paper we first present a fast algorithm to determine the consistency of three silhouettes from known (but arbitrary) viewing directions, assuming the projection is scaled orthographic. The temporal complexity of the algorithm is linear in the number of points of the silhouette boundaries. We further prove that a set of more than three convex silhouettes are consistent if and only if any three of them are consistent. Another possible application of our approach is to determine the miscalibrated cameras in a large camera system. A consistent subset of cameras can be determined on the fly and miscalibrated cameras can also be recalibrated at a coarse scale. Real and synthesized data are used to demonstrate our results.