Closed-loop multiple view registration

In this study, a novel algorithm is presented for multiple view registration with a loop constraint. Instead of estimating the global pose of each view, the proposed algorithm is designed via the analysis of relative poses. Our method proves that the rotation and translation components can be exactly decoupled and further derivation reveals the mechanism of how the influence of a single update of rotation on one view of the loop will be propagated into the whole loop, resulting in an efficient, accurate and robust performance even for complicated cases such as 1000 views in a loop. Meanwhile, Lagrange multiplier is utilized so that the loop constraint is satisfied and the matrix exponentiated gradient method is used to optimize the solution. Our method is implemented in an iterative way, where the rotation matrices are updated on manifold so that their orthonormality can be well preserved in each iteration. The algorithm is verified by a series of tests and experimental results demonstrate the effectiveness and convergence of our algorithm.