Conjugate Gradient Bundle Adjustment

Bundle adjustment for multi-view reconstruction is traditionally done using the Levenberg-Marquardt algorithm with a direct linear solver, which is computationally very expensive. An alternative to this approach is to apply the conjugate gradients algorithm in the inner loop. This is appealing since the main computational step of the CG algorithm involves only a simple matrix-vector multiplication with the Jacobian. In this work we improve on the latest published approaches to bundle adjustment with conjugate gradients by making full use of the least squares nature of the problem. We employ an easy-to-compute QR factorization based block preconditioner and show how a certain property of the preconditioned system allows us to reduce the work per iteration to roughly half of the standard CG algorithm.