# Point Cloud Segmentation from iPhone-Based LiDAR Sensors Using the Tensor Feature
## 3 Methodology
### The Algorithm of the Point Cloud Segmentation Workflow
In the comparison, the point cloud segmented by the proposed method outperforms others, where the ground and different objects are successfully segmented, although the results are a little over-segmented due to the noisy point cloud samplings. Moreover, in the point cloud segmentation procedure, the noisy point cloud samplings acquired from the iPhone LiDAR sensor are successfully segmented into different parts. With the line saliency, the line features are extracted, and different surface segments are generated based on the surface saliency, after the denoising process based on the point saliency. Figure 6.0

As a quantified measure, \(F_{score}\) is a widely used accuracy index to measure the performance of the algorithm, as shown in Equation (18); hence, it is applied here to evaluate the accuracy of point segmentation results with different methods. Here, the _precision_ of \(F_{score}\) is computed based on points in each segmented result and the number of points which truly belong to the related plane, and the _recall_ is computed based on points in each segmented result and the number of the points in the related ground truth segments. To compute the detailed accuracy description, the _precision_, _recall_, and \(F_{score}\) of each segmentation result are computed based on the ground truth segmentation in Figure 11a. The \(F_{score}\) for each part of the segmentation result is illustrated in Figure 6.1 As seen in the figure, the lighter (yellower) the color, the higher the \(F_{score}\), while the darker (redder) the color, the lower the \(F_{score}\). The ground part of the segmentation result in Figure 11a is lighter than that of the result in Figure 11b,c, but in other parts, the situation becomes complex: some parts of the image are darker in one method than in the same part of another, while in other parts this is not the case. However, compared with Figure 11d, the results become definite and clear: most of the parts are lighter than others and the results outperform others. The statistics of _precision_, _recall_, \(F_{score}\) of each part in the segmentation result is further conducted, and the average values are computed and illustrated in Figure 6.2 Due to the diverse number of the segmentation results, the average values are calculated for each method. As seen in Table 1, the average _precision_ of the proposed method is 0.8230, which is a little lower than that of [PERSON] [9], [PERSON] [21], and [PERSON] [22] with an average _precision_ of 0.8133. However, the average _recall_ of the proposed method is 0.4250, which is the highest in the comparison, and that of the [PERSON] [9], [PERSON] [21], and [PERSON] [22] is 0.0987. Hence, the average \(F_{score}\) for the proposed method by [PERSON] [18], [PERSON] [19] and [PERSON] [20], [PERSON] [9], [PERSON] [21], and [PERSON] [22], are 0.4828, 0.2963, 0.2579, and 0.1359, respectively. From the statistics, the proposed method overall performs better than the other methods, which is consistent with the result in Figure 6.3

### Point Cloud Segmentation for the Dataset in the Large Area

Since the main purpose of the method is to segment the point cloud into different plane structures, to verify the capability of the proposed point cloud segmentation method, the other dataset is obtained from the iPhone-based LiDAR sensor, in an area of 22.78 m\({}^{2}\), with 141,837 points, as depicted in Figure 12a. It is a stairway scene, and is divided into 31 parts in ground truth segmentation, as depicted in Figure 12b. The point cloud segmentation results of different methods are depicted from Figure 12c-f. In Figure 12c, the dataset is segmented into 295 parts, using the automatically computed parameter [Max angle: 10\({}^{\circ}\), Max relative distance: 2.0 m, Max distance: 0.1 m, Min points per facet: 10, Max edge length 0.07] by the algorithm. To obtain the optimal searching distance, set \(\mathbf{r}\in\mathbf{[0.1,0.3]}\) m for the methods by [PERSON] [19] and [PERSON] [20], and [PERSON] [9], [PERSON] [21] and [PERSON] [22].