# 3-D Point Cloud Registration Using Convolutional Neural Networks
## 2 Related Work
Additionally, a registration algorithm by using the hand and soft assignments to improve the robustness and accuracy for partially overlapping point cloud registration was proposed in Reference [26]. To extend the robustness to noise and/or outliers, the Trimmed ICP approach was presented in Reference [27] that applied the Least Trimmed Squares algorithm in all stages of the operation. In Reference [28], [PERSON] et al. presented the Fraction ICP method that can robustly identify and discard outliers and guarantee the convergence to a locally optimal solution. The other existing approach, Efficient Sparse ICP method, using sparsity-inducing norms to considerably improve robust registration caused by noise and outliers whilst employing a Simulated Annealing search in order to efficiently resolve the underlying optimization problem was proposed in Reference [29]. [PERSON] et al. [30] developed the ICP-based algorithm integrating with a branch-and-bound (BnB) principle to figure out the globally optimal solution for Euclidean registration between two 3-D surfaces or 3-D point clouds starting from any initialization. Scale-ICP approach integrating a scale factor with the original ICP method was proposed in Reference [31] so as to accurately perform the registration between two 3-D point clouds in the case of large-scale stretches and noises. [PERSON] et al. [32] developed a multi-directional affine registration (MDAR) algorithm by using the statistical characteristics and shape features of point clouds for affine registration problem. In addition to the aforementioned distance-minimization-based registration algorithms, another registration approach using distinct features extracted from 3-D point cloud data sets was also presented in References [33; 34; 35; 36], to robustly and efficiently enhance the registration problem. Particularly, many feature descriptors including local-based descriptor, global-based descriptor and hybrid-based descriptor were presented in recent years and a comprehensive review of the existing algorithms can be sought in Reference [37]. Nevertheless, the aforementioned existing algorithms all are based on randomly selecting different points in two 3-D point clouds to form a pair of corresponding bases in rough registration phase whilst iteratively minimizing the distance between two 3-D point clouds until the convergence within the desired tolerance of ICP-based methods in the precise registration phase. These are the reasons why those algorithms cannot be employed in real-time closed-loop object picking and assembly systems due to their slow computation. In addition to the aforementioned algorithms, there are some approaches related to point cloud registration using deep learning which were developed in recent years. In Reference [38], a point cloud registration method using a deep neural network auto-encoder for outdoor localization between a close-proximity scanned point cloud and a large-scale point cloud was proposed. Specially, [PERSON] et al. [39] developed an efficient and robust point cloud registration architecture, PointNetLK architecture, based on an iterative image registration approach [40] and PointNet architecture [9]. However, the PointNetLK architecture involved iterative computation with the number of iterations in accordance with a minimum threshold of the optimal twist parameters. In this paper, a seemingly novel efficient algorithm using deep learning is proposed to accelerate the estimation time while maintaining the required accuracy. The key contributions of this research can be summarized as follows:  
1. We propose a seemingly novel registration architecture including 3-D convolutional neural networks (3-D CNNs) for the rough registration stage and 2-D CNNs for the precise registration stage that transforms the 3-D point cloud registration problem to a regression problem with estimated outputs as angular disparities between the model point cloud and a data point cloud. 2.