  In this paper, by modeling the point cloud registration task as a Markov
decision process, we propose an end-to-end deep model embedded with the
cross-entropy method (CEM) for unsupervised 3D registration. Our model consists
of a sampling network module and a differentiable CEM module. In our sampling
network module, given a pair of point clouds, the sampling network learns a
prior sampling distribution over the transformation space. The learned sampling
distribution can be used as a "good" initialization of the differentiable CEM
module. In our differentiable CEM module, we first propose a maximum consensus
criterion based alignment metric as the reward function for the point cloud
registration task. Based on the reward function, for each state, we then
construct a fused score function to evaluate the sampled transformations, where
we weight the current and future rewards of the transformations. Particularly,
the future rewards of the sampled transforms are obtained by performing the
iterative closest point (ICP) algorithm on the transformed state. By selecting
the top-k transformations with the highest scores, we iteratively update the
sampling distribution. Furthermore, in order to make the CEM differentiable, we
use the sparsemax function to replace the hard top-$k$ selection. Finally, we
formulate a Geman-McClure estimator based loss to train our end-to-end
registration model. Extensive experimental results demonstrate the good
registration performance of our method on benchmark datasets.
