# Color Point Cloud Registration Algorithm Based on [PERSON]
## 4 Experiment  
### Point Cloud Registration  
The experimental environment is Visual Studio 2015, using Open3D point cloud library, the operating system is Windows 10, and computer hardware configuration is Intel Core i9-7980 XE CPU, 32 GB memory. According to algorithm [14], the experimental parameters are set as follows: the scalar factor \(\sigma=30\), the maximum number of iterations is set to 90, and the threshold of the error function is set to \(10^{-6}\). Figure 5 shows two randomly selected point clouds from the existing dataset [14] and the registration result of the different algorithms. Figure 5a,b are the source and target point cloud, respectively. Figure 5d shows the result through the traditional Point-to-Plane ICP [19]. The result is wrong because the overlap part of two point clouds are not spliced very well. This is because source and target point cloud have too much similar geometric structure such as ground and wall, and they cannot be registered without color information. Moreover, under different collection positions with various lighting conditions, the color information of the overlapping parts of the two point clouds varies greatly, which is obvious in (a) and (b). The error function of [14] using gray as color information will lead to the wrong direction during the iterative optimization process and gain a local optimal result, as shown in Figure 5c. However, as we mentioned previously, the hue is robust to light and has little difference in different lighting conditions. Hence, it would strictly constrain the convergence direction during the optimization process and finally obtain the correct result, as shown in Figure 5g. Figure 5e,f show the results of improved DeepICP [8] and DCP [9] based on the neural network, respectively. We use the pre-trained model in their paper and  
apply it to these two point clouds. It can be seen that the results are not appropriate and this is because the deep-learning method relies on the dataset very much and may perform well using one kind of data but not another kind. Their training dataset is CAD models and not scene datasets. The common evaluation criterion for point cloud registration is Root Mean Square Error (RMSE). Given two scene fragments \((P_{i},P_{j})\), their correspondence is \(\mathcal{K}_{ij}\), then RMSE under the rigid transformation \(\zeta_{ij}=(w_{ij},t_{ij})\) is as follows:  
\[RMSE(\mathcal{K}_{ij},\zeta_{ij})=\sqrt{\frac{1}{\mathcal{K}_{ij}}\sum_{(p,q) \in\mathcal{K}_{ij}}\|R(w_{ij})p+t_{ij}-q\|^{2}} \tag{22}\]  
It can be seen that RMSE represents the difference between corresponding points of the two point clouds, and the smaller it is, the higher the registration accuracy. Figure 5: The registration results of the two random point clouds from dataset [14]: (**a**) source point cloud and (**b**) target point cloud. Registration results of (**c**) algorithm [14] (RMSE = 0.010607), (**d**) algorithm [20] (RMSE = 0.020071), (**e**) DeepICP (RMSE = 0.031654), (**f**) DCP (RMSE = 0.043145), and (**g**) ours (RMSE = 0.006683). Given two scene fragments, if the resulting rigid transformation \(\xi_{ij}=(w_{ij},t_{ij})\) and the true rigid transformation \(\xi_{ij}^{*}\) is close enough, the rigid transformation is correct. \(\mathcal{K}_{ij}^{*}\) is the correspondence under the true transformation \(\xi_{ij}^{*}\). If the RMSE of \(\mathcal{K}_{ij}^{*}\) under the transformation \(\xi_{ij}\) is smaller than the given threshold \(\tau\), \(\xi_{ij}\) is correct:  
\[RMSE(\mathcal{K}_{ij}^{*},\xi_{ij})<\tau \tag{23}\]  
The dataset used is RGB-D ScenesV2 [13], and each frame contains depth information, color information, and the ground truth transformation matrix of the current frame. Five scenes are selected in this experiment. All of them are point clouds obtained by the RGBD camera scanning indoor scenes. Each frame has slightly different lighting conditions at different viewpoints. For each of the five selected scenarios, 60 frames are selected as test data equidistantly.