Generalizing Inverse Compositional and ESM Image Alignment

Inverse compositional (IC) image alignment (Baker and Matthews in Int. J. Comput. Vis. 56(3):221–255, 2004) uses the symmetry between the roles of the fixed and moving images for faster processing. However, it requires implementation of compositional optimizer update steps. The IC approach can be viewed as an efficient way of computing the similarity measure derivative relative to the fixed image warp parameters. Since the mapping between the fixed and moving warp parameters is continuous and differentiable, this derivative can be converted into the moving warp space using the chain rule. This avoids the need for compositional update steps. Our generalization also allows the efficient second order method (ESM) (Malis in Proceedings of the 2004 IEEE International Conference on Robotics and Automation (ICRA04), pp. 1843–1848, 2004; Benhimane and Malis in IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004; Malis and Benhimane in Robot. Auton. Syst. 52(1):39–52, 2005) to be applied to general parameterizations of the transformation. Experiments using multiple similarity measures and optimizers show that our generalized IC method equals or exceeds the performance of the original IC approach. The generalized ESM approach is more reliable than the classic approach as it increases the capture radius of the optimization.