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Recent advances in 3D vision have demonstrated the strengths of photometric bundle adjustment. By directly minimizing reprojected pixel errors, instead of geometric reprojection errors, such methods can achieve sub-pixel alignment accuracy in both high and low textured regions. Typically, these problems are solved using a forwards compositional Lucas-Kanade [7] formulation parameterized by 6-DoF rigid camera poses and a depth per point in the structure. For large problems the most CPU-intensive component of the pipeline is the creation and factorization of the Hessian matrix at each iteration. For many warps, the inverse compositional formulation can offer significant speed-ups since the Hessian need only be inverted once. In this paper, we show that an ordinary inverse compositional formulation does not work for warps of this type of parameterization due to ill-conditioning of its partial derivatives. However, we show that it is possible to overcome this limitation by introducing the concept of a proxy template image. We show an order of magnitude improvement in speed, with little effect on quality, going from forwards to inverse compositional in our own photometric bundle adjustment method designed for object-centric structure from motion. This means less processing time for large systems or denser reconstructions under the same real-time constraints. We additionally show that this theory can be readily applied to existing methods by integrating it with the recently released Direct Sparse Odometry [4] SLAM algorithm.

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