Reweighted Discriminative Optimization for least-squares problems with point cloud registration

Optimization plays a pivotal role in computer graphics and vision. Learning-based optimization algorithms have emerged as a powerful optimization technique for solving problems with robustness and accuracy because it learns gradients from data without calculating the Jacobian and Hessian matrices. The key aspect of the algorithms is the least-squares method, which formulates a general parametrized model of unconstrained optimizations and makes a residual vector approach to zeros to approximate a solution. The method may suffer from undesirable local optima for many applications, especially for point cloud registration, where each element of transformation vectors has a different impact on registration. In this paper, Reweighted Discriminative Optimization (RDO) method is proposed. By assigning different weights to components of the parameter vector, RDO explores the impact of each component and the asymmetrical contributions of the components on fitting results. The weights of parameter vectors are adjusted according to the characteristics of the mean square error of fitting results over the parameter vector space at per iteration. Theoretical analysis for the convergence of RDO is provided, and the benefits of RDO are demonstrated with tasks of 3D point cloud registrations and multi-views stitching. The experimental results show that RDO outperforms state-of-the-art registration methods in terms of accuracy and robustness to perturbations and achieves further improvement than non-weighting learning-based optimization.