# Point Cloud Segmentation from iPhone-Based LiDAR Sensors Using the Tensor Feature
## 3 Methodology
### The Algorithm of the Point Cloud Segmentation Workflow  
Based on the processing stages of tensor features, the algorithm of the point cloud segmentation workflow is composed of three main steps, including normal vector computation, tensor aggregation, and point segmentation, which are depicted in Algorithm 1. ``` Point cloud Segmentation based on the Tensor Feature \(\textbf{PSTF}(P,r)\) INPUT: point cloud \(P\), the searching distance for the neighborhood \(r\), segmentation thresholds \(\{\textbf{\eta}_{point\_Hine}\textbf{\_}{\textit{Psurface}},\theta_{surfac}\}\) OUTPUT: segmented point cloud sets \(P_{\textit{Seg}}\)//Stage : Normal vector computation based on initial tensor encoding FOREACH\(\textbf{p}\) in \(\textbf{P}\)\(\boldsymbol{\Omega}\{\textbf{\emph{p}}_{i}\|\textbf{\emph{p}}_{p}-\textbf{ \emph{p}}_{i}\|\leq\textbf{\emph{r}}\}=\text{GetNeighborhood}(\textbf{\emph{p}}, \textbf{\emph{r}})\);// get the neighborhood of \(\textbf{\emph{p}}\)\([\overrightarrow{\textbf{\emph{



initially encoded tensor. The tensor at each point is re-encoded using normal information and aggregated from its neighborhood, followed by tensor feature decomposition and shape classification operations. Finally, the point cloud segmentation method is conducted using the clustering process, along with comparisons and a discussion. ### Datasets from the iPhone-Based LiDAR Sensor

In this paper, point cloud data are obtained from the LiDAR sensor included with the iPhone 12 Pro Max, which is a kind of consumer electronic device, as depicted in Figure 5. The LiDAR sensor is a solid-state device with a range of 5 m and low resolutions, and the point cloud data are obtained based on TOF (Time of Flight) technology. In the first experiment, the dataset is in a small scene consisting of three cubes on the ground with an area of 1.49 m\({}^{2}\), and the point number is 15,599, as depicted in Figure 6. In addition, the dataset is affected by the noisy point cloud samplings by the LiDAR sensor. Hence, as the data quality index, the standard deviation (std.) is computed based on the distribution of the point cloud on a flat plane, which is acquired from the datasets with a flat area. In the dataset, the mean square error is 0.0018 m.

### Normal Vector Computation and Refinement Based on the Tensor Feature Encoding

There are two steps for the normal vector computation, after setting the searching distance \(r\) at 0.3 m. First, normal vectors are computed from the scatted points using the initial tensor encoding, and the eigenvectors with the largest eigenvalues are used as the normal vector; secondly, the initially computed normal vectors are re-encoded into the tensor, and the normal vectors are re-computed and refined in a similar way to the first step. As depicted in Figure 7, the normal vectors are computed using the parameter \(\sigma=0.1\). Although it is a flat area the normal vectors are in a specific direction, there are many normal vectors with chaotic normal directions, which are caused by the noisy data samplings,

Figure 5: The LiDAR sensor included in the iPhone. Figure 6: The dataset acquired by the LiDAR sensor. as shown in Figure 7, enlarged view \(a\). Hence, a refinement process is conducted, and the normal vectors are re-computed and refined. In the refined result, the direction of the normal vector becomes more regularized in the flat plane, compared with the first computed result. ### Shape Description Using the Tensor Analyzing

The tensor at the point \(p\) is aggregated from its neighborhood with the normal information encoded, and the geometric structures in each dimension are propagated to \(p\). After the tensor aggregation process, the tensor at each point is decomposed into 1-dimensional, 2-dimensional, and 3-dimensional geometric features, as depicted in Figure 8.

As seen in Figure 8, there are three types of geometric features in the dataset and each has related saliency figure.