Model-Based Pose Estimation by Consensus

We present a system for determining a consensus estimate of the pose of an object, as seen from multiple cameras in a distributed network. The cameras are pointed towards a 3D object defined by a configuration of points, which are assumed to be visible and detected in all camera images. The cameras are given a model defining the 3D configuration of these object points, but do not know which image point corresponds to which object point. Each camera estimates the pose of the object, then iteratively exchanges information with its neighbors to arrive at a common decision of the pose over the network. We consider eight variations of the consensus algorithm, and find that each converges to a more accurate result than do the individual cameras alone on average. The method exchanging 3D world coordinates penalized to agree with the input model provides the most accurate results. If bandwidth is limited, performing consensus over rotations and translations requires cameras to exchange only the six values specifying the six degrees of freedom of the object pose, and performing consensus in SE(3) using the Karcher mean is generally the best choice. We show further that interleaving pose calculation with the consensus iterations improves the final result when the image noise is large.