# 3-D Point Cloud Registration Using Convolutional Neural Networks
## 6 Experiments  
In this section, experimental results for 3-D point cloud registration are provided to validate the proposed registration algorithm based on CNN architectures. In particular, when it comes to point cloud data, open data including \"Bunny\", \"Dragon\" & \"Buddha\", \"Armadillo\" and \"Horse\" from the Stanford 3-D Scanning Repository [42; 43; 44] and NTU CSIE [45], respectively, are employed. Besides, two algorithms such as the \"RANSAC then ICP\" (RANSAC+ICP) algorithm using Fast Point Feature Histograms (FPFH) [46] to describe features for point clouds and the \"Fast Global Registration\" (FGR) algorithm [47] provided in Open3D [48; 49], a modern library for 3-D data processing, are applied to evaluate the performance of the proposed algorithm. Moreover, in order to give the quantitative evaluation, in addition to the computation time, the mean squared error (MSE) value used to compare the matching rate among these methods is given as follows [22]. \[MSE=\frac{1}{m}\sum_{j=1}^{m}||\mathbf{p}_{i}-\mathbf{q}_{j}|| \tag{8}\]  
where \(m\) is the number of points in the data point cloud and \(\mathbf{p}_{i}\) and \(\mathbf{q}_{j}\) stand for the corresponding closest points in the model point cloud and the data point cloud, respectively. All programs performing these approaches are programmed in Python on an Intel Core i9-9900K CPU @3.6 GHz PC equipped with a GeForce RTX 2080 Ti SEA HAWK X Graphics Processing Unit (GPU). In the training process, for each of point cloud data, it takes about 6 hours and 3 hours to train a 3-D CNN model for the rough registration and a 2-D CNN model for the precise registration, respectively. Nevertheless, transfer learning can be employed to reduce the training time of CNN models for a new 3-D point cloud data. After training, 20 unforeseen samples which are generated by randomly rotating and translating, followed by downsampling the model point cloud, according to each of these five data sets including Bunny, Horse, Dragon, Buddha and Armadillo are employed to validate the performance of the trained CNN models as well as two other approaches such as RANSAC+ICP and FGR approach. Table 1 shows a comparison on the MSE and computation time for test samples from 1 to 10 of Bunny data whilst the similar comparison for test samples from 11 to 20 is given Table 2 where \(n\) and \(m\) stand for the number of points in the model and data point cloud, respectively. When it comes to the MSE, the smaller MSE is, the better registration result is. Generally, it is noticeable that from all the three algorithms, FGR algorithm gives the worst result in terms of MSE value whereas the results of the proposed approach are a little bit worse than RANSAC+ICP method. Particularly, although FGR method shows the smaller computation time compared with RANSAC+ICP method, MSE values according to this method are quite large with three imprecise estimations observed in samples 3, 14 and 15. Besides, the maximum MSE value at approximately 3.418 mm in sample 3 and the minimum MSE at around 2.851 mm in sample 8 experienced in the proposed algorithm shows the lowest disparity, nearly 0.567 mm, in all estimations of 20 test samples while these differences are witnessed at around 1.063 mm and 11.442 mm in accordance with RANSAC+ICP and FGR approach, respectively. This shows that the developed registration architecture possesses the best stable result in estimating the transformation between two 3-D point clouds in the case of Bunny data. In addition to this advantage, obviously, the smallest computation time is also experienced in the proposed algorithm with the largest value at around 0.027 s whilst it takes approximately 0.140 s and 0.028 s (an imprecise estimation) for the fastest estimation in the case of RANSAC+ICP and FGR approach, respectively. Similar to Bunny data, comparable results on two benchmarks including the MSE and computation time for these three algorithms are shown in Tables 3-10 for Horse, Dragon, Buddha and Armadillo data, respectively.