# Point Cloud Segmentation from iPhone-Based LiDAR Sensors Using the Tensor Feature
## 3 Methodology
### The Algorithm of the Point Cloud Segmentation Workflow
Hence, the point cloud in Figure 12d is segmented into 263 parts, and in Figure 12e, the number of the segmented parts is 306 parts. With the neighborhood searching distance r = 0.3m, the tensor feature for the point cloud dataset is computed, re-encoded, aggregated, and decomposed, based on the proposed method. In addition, there is no shortcut to obtaining the optimal values for \(\mathbf{\eta}_{point}\mathbf{J}_{line}\mathbf{\eta}_{surface}\), while these values are suggested to be 80% of the maximum saliency in each related dimension. Using the segmentation thresholds \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Different Methods** & **Average _Precision_** & **Average _Recall_** & **Average _F\({}_{score}\)_ \\ \hline [PERSON] [18] & 0.6797 & 0.3104 & 0.2963 \\ [PERSON] [19] and [PERSON] [20] & 0.8133 & 0.2414 & 0.2579 \\ [PERSON] [9], [PERSON] [21] & 0.8779 & 0.0987 & 0.1359 \\ and [PERSON] [22] & 0.8230 & 0.4250 & 0.4828 \\ The proposed method & \multicolumn{1}{c}{} & & \\ \end{tabular}
\end{table} 
Table 1: The _F\({}_{score}\)_ computation results. Figure 11: The _F\({}_{score}\)_ of each part in comparison with different segmentation methods. (**a**) The _F\({}_{score}\)_ of the segmentation result by [PERSON] [18]; (**b**) The _F\({}_{score}\)_ of the segmentation result by [PERSON] [19] and [PERSON] [20]; (**c**) The _F\({}_{score}\)_ of the segmentation result by [PERSON] [9], [PERSON] [21], and [PERSON] [22]; (**d**) The _F\({}_{score}\)_ of the segmentation result by the proposed method. \(\{\eta_{point}=30.\eta_{line}=35.\eta_{surface}=200,\theta_{surface}=10^{\circ}\}\), the point cloud dataset is segmented into 111 parts, as depicted in Figure 12f. As seen in Figure 12, the point cloud dataset is segmented into different parts, and the segmented parts with the point number lower than 20 are not labeled. In the results presented in Figure 12c,e, the points on the left are segmented, and there is a large area that is successfully segmented (labeled in brown and blue in each picture), while on the right side, some are over-segmented, and some are not. In Figure 12d, the left side of the dataset is over-segmented and labeled in different colors, while the right side seems to be under-segmented with few colored labels. In Figure 12f, the point cloud dataset is successfully segmented, although some parts are not properly segmented. To visualize the segmentation performance, each part of the segmentation result based on different methods is labeled in a graded color according to the \(F_{score}\), as depicted in Figure 13.

Figure 12: The comparison of different point cloud segmentation methods. (**a**) The dataset with texture information; (**b**) Ground truth segmentation of the dataset; (**c**) Segmentation result by [PERSON] [18]; (**d**) Segmentation result by [PERSON] [19] and [PERSON] [20]; (**e**) Segmentation result by [PERSON] [9], [PERSON] [21], and [PERSON] [22]; (**f**) Segmentation result by the proposed method. As seen in Figure 13, the lighter (yellow) the color, the higher the \(F_{score}\), and vice versa. There is a part in the left side of Figure 13a with the lightest color than that in the other results, and the right side of Figure 13b is with the darkest color in all the results. The result in Figure 13c seems good when compared with the results in Figure 13b; however, the point cloud dataset is well segmented both in the left and the right side of Figure 13d, which shows the best performance among the results. The statistics of average _precision_, average _recall_, average \(F_{score}\) of each part in the segmentation result are further computed, and the result is illustrated in Table 2.

As seen in Table 2, the average _precision_ of [PERSON] [9], [PERSON] [21], and [PERSON] [22] is 0.9527, which holds a higher value than others, and it also performs well in the result of [PERSON] [19] and [PERSON] [20]. However, the average _recall_ of these two methods are 0.0369 and 0.0177, respectively.