Rapid analytic optimization of quadratic ICP algorithms
This paper discusses the efficient optimization of iterative closest points (ICP) algorithms. While many algorithms formulate the optimization problem in terms of quadratic error functionals, the discontinuities introduced by varying changing correspondences usually motivate the optimization by quasi-Newton or Gauss-Newton methods. These disregard the fact that the Hessian matrix in these cases is constant, and can thus be precomputed analytically and inverted a-priori. We demonstrate on the example of Allen et al.'s seminal paper ""The space of human body shapes"", that all relevant quantities for a full Newton method can be derived easily, and lead to an optimization process that reduces computation time by around 98% while achieving results of almost equal quality (about 1% difference). Along the way, the paper proposes minor improvements to the original problem formulation by Allen et al., aimed at making the results more reproducible.