# Point Cloud Registration Algorithm Based on Adaptive Neighborhood Eigenvalue Loading Ratio
## 3 Experiment
### Results
#### 3.3.3 Point Cloud Registration Algorithm Based on Feature Point Similarity Formula
The root-mean-square error (RMSE) [29] was employed as the evaluation metric for the experiments, which calculated the sum of the squared distances between corresponding point pairs in the source and target point clouds. Additionally, the registration time required was compared to assess the efficiency of the registration algorithm. The RMSE was used as a metric for calculation, as shown in Formula (10):  
\[RMSE=\sqrt{\frac{1}{n}{\sum\limits_{i=1}^{n}{\left\|{R_{pi}+t-q_{i}}\right\|^ {2}}}} \tag{10}\]  
A comparison of the registration results between four algorithms is presented in Figure 8: the ICP (iterative closest point) algorithm, the ColorICP (color iterative closest point) algorithm, the FPFH+ICP (fast point feature histogram combined with ICP) algorithm, and the algorithm proposed in this study. The performance of the four algorithms was evaluated in six scenarios:  
1. The ICP algorithm: The traditional ICP algorithm operates by iteratively minimizing the geometric distances between point clouds to achieve registration. It depends on the initial registration and is sensitive to noise, which can lead to convergence on a local optimum. Consequently, satisfactory registration was not obtained in any of the six scenes. 2. The ColorICP algorithm: This algorithm incorporates color information into the ICP process for point cloud registration. As can be seen from the results, the color information could somewhat enhance registration accuracy, particularly in models with rich color variations (e.g., bear dolls and tree benches). However, in areas where color overlap was not significant, especially in pure color scenes, such as rabbits and dragons, its performance improvement was limited. 3. The FPFH+ICP algorithm: This approach enhances ICP registration by incorporating local geometric features, and greatly improves the registration of complex geometries. It showed considerable improvement over the basic ICP and ColorICP algorithms. Nevertheless, it still encountered difficulties with specific details and when local features were not pronounced or the point cloud was heavily occluded. 4. The algorithm in this study: In all scenes, the algorithm proposed in this study achieved superior registration results, with closer and more precise registration between the source and target point clouds. In the \"dragon\" and \"tree bench\" scenarios, the algorithm handled complex geometric structures effectively, resulting in more accurate registration, while in complex scenes (e.g., the chamber or office), it is evident that the registration was more precise than the other algorithms, with a major reduction in misregistration. In summary, the traditional ICP algorithms are prone to fall into locally optimal solutions when dealing with complex point cloud data. The ColorICP algorithm and the FPFH+ICP algorithm enhanced the accuracy and robustness of registration to some extent by incorporating color information and local geometric features, respectively. The algorithm proposed in this study improved the registration accuracy under complex geometric structures and varied color distributions and demonstrated adaptability and stability in a range of scenarios. It exhibited major advantages, particularly in point cloud registration scenarios characterized by complex geometries and changing colors, such as the \"dragon\" scenario. From the data comparison of the registration results, as shown in Table 3, the following observations can be made:  
Figure 8: Comparison of the registration effects of the four types of algorithms in different scenarios, the best performance figures are highlighted in bold font. 1. The ICP algorithm: The ICP algorithm generally exhibited a higher root-mean-square error (RMSE) and longer runtime in different datasets, indicating that it is less precise and efficient in processing complex datasets. In particular, the ICP algorithm is prone to failure at low overlap rates. 2.