## 4 Verification and Analysis  
### Registration Visualization  
In order to test the effectiveness of the proposed algorithm, the data sets Bunny (40256) and Monkey (125952) from Stanford University were adopted for simulation. The initial state of the point cloud is shown in Figure 4. The model computer used in the test is I5-10400F, configured with a memory of 16G, a display card of Nvidia GTX 1060 6G, an operating system of win10 64 bit, and is operated on VS2019. The target point cloud was rotated \(-50\) degrees on the Z axis, and shifted 5 mm in X and Y directions, respectively, but \(-10\) mm in the Z direction, which was then used as a point cloud to be registered. The downsampling grid size was set to 0.05 mm. Since the initial alignment results obtained by the method in the literature [21] have a large deviation, the alignment accuracy and  
Figure 3: Flowchart for the initial registration of RANSAC by IWOA+ accurate registration of the improved ICP. speed were further compared in this paper. and the proposed algorithm was compared to standard ICP, RANSAC algorithms, Depth Filtering-ICP. The initial state of the point cloud is shown in Figure 4.  
The maximum number of iterations of ICP, RANSAC, Depth Filtering- ICP and IWOARANSAC-ICP algorithms was all set as 50. In IWOA algorithm, set 20 times iterations, 10 whale populations and a 0.05 threshold of fitness function \(m_{l}\) were set. For the research objects of this paper, characteristic quantities \(f\) were selected as the evaluation index in order to evaluate the algorithm. It is \([50,1000]\) for the value range of characteristic quantity \(f\) in this paper, which was used for histogram feature quantity evaluating feature points. We can express the feature evaluation function \(f_{k}\) of point cloud as follows:  
\[f_{k}=k_{1}+3*k_{2} \tag{22}\]  
Among which \(k_{1}\) is determined by the angle between the normal vector of any point and that of its adjacent point. Moreover, the plane is divided into \([0,\pi/3][\pi/3,2\pi/3]\)\([2\pi/3,\pi]\), and \(k_{1}\) is noted as 1,2,3 according to the range of angle between the normal vector and that of its adjacent point. \(k_{2}\) is the Euclidean distance between any point and the nearest adjacent point. If the distance is one that is greater than a certain threshold value and zero that is less than the threshold value, the threshold value was set to 0.005 in this paper. Then we established a histogram with an interval number that two multiple by 3 equals six to obtain the corresponding 6-dimensional characteristic value in accordance with the classifications of these two feature values. We regarded the percentage occupying the total number of the points of the point cloud in each interval as the corresponding interval value and characteristic value. The default values were adopted for other parameters, which \(f_{k}\) were 16 before optimization. Moreover, it was 0.500000 for the fitness function value. It was 0.000015 for the evaluation function value. After optimization, they \(f_{k}\) were 42, 0.239051, and 0.000006, respectively, for the default value, the fitness function value, and the evaluation function value. For convergence curve of the optimized RANSAC algorithm of IWOA, it is shown in Figure 5.  
It can be seen from the iteration curve that it can quickly obtain the optimal solution after the start of iteration for the optimized RANSAC algorithm of IWOA. It is less than that of the simple RANSAC algorithm for the fitness value of this algorithm, which has a faster speed of convergence, stable curve, and good real-time performance. The registration results of the four registration methods are shown in Figure 6.  
Figure 4: Initial state of point cloud. (a) Bunny; (b) Monkey. According to Figure 6, the standard ICP algorithm and the three standard algorithms are all capable of completing the registration of Bunny and Monkey point clouds.