# Geometric Accuracy Evaluation Method for Subway Stations Based on 3D Laser Scanning

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Registration Issues

#### 2.1.1. Registration between Point Clouds

#### 2.1.2. Registration between Point Clouds and BIM

#### 2.2. Geometric Accuracy Evaluation

## 3. Research Method

#### 3.1. Overview

- A coarse registration based on a grid is used to convert the point cloud to the survey coordinate system predefined in BIM;
- The point-to-line iterative closest point (PL-ICP) algorithm based on the inner wall lines is used to achieve fine registration;
- The structural elements of the subway station are extracted from the point cloud;
- The evaluation indexes are proposed and statistically analyzed for geometric accuracy evaluation.

#### 3.2. The Coordinate Registration of the Point Cloud and BIM

#### 3.2.1. Coarse Registration Based on Grid

_{θ}is the empirical threshold (set to 10° in this study). If condition 1 is satisfied, the line to be measured will be marked as parallel; if condition 2 is satisfied, the line to be measured will be marked as perpendicular.

_{0}(α

_{x}, α

_{y}, 0) and the quadrant angle is θ

_{1}; the point cloud center is represented as p

_{1}(β

_{x}, β

_{y}, 0) and the quadrant angle is θ

_{2}. Then, the point cloud is transformed into the predefined survey coordinate system in BIM by Equation (2). The coarse registration process is shown in Figure 3. After horizontal registration, the z-axis is adjusted according to the height of the top and bottom slabs.

#### 3.2.2. Fine Registration between Point Cloud and BIM

_{k}= $\left[\begin{array}{cc}{R}_{k}& {t}_{k}\\ 0& 0\end{array}\right]$, p

_{i}is the 3D coordinate of the target point of the design model, p

_{i}′ is the midpoint of the line connecting the two nearest target points in the point cloud, and n

_{i}is the normal vector of p

_{i}′.

_{k}is obtained using the PL-ICP algorithm, a coordinate transformation is performed on the coarse matching point cloud using transformation matrix T

_{k}. Note that if the coarse registration step is omitted, it may lead to an upside-down situation in the point cloud registration [54]. Through the above steps, the registration of the point cloud with BIM is finally achieved.

#### 3.3. Subway Station Structure Element Extraction

_{i}of that voxel. After all the voxels are searched, the down-sampled point cloud model P′ is derived. Subsequently, element extraction is performed on the point cloud model P′ to obtain the facade, slab, and structural column information.

_{th}are marked as the current region, and the points that meet the residual threshold r

_{th}are marked as the candidate seed points. After the search of all the nearest neighbors is completed, the next available seed is accessed from the list of candidate seed queues, and the above operation is repeated until all points are labeled. A region growth of subway station structure element extraction is shown in Figure 5, where ${\overrightarrow{n}}_{i}$, ${\overrightarrow{n}}_{j}$, and ${\overrightarrow{n}}_{k}$ are the normal vector of each initial seed, and different structure surfaces, i.e., facades, slabs, and structural columns, are extracted using the region growing algorithm. Moreover, the surfaces of different structures are shown in different colors.

#### 3.4. Geometric Accuracy Evaluation Index

#### 3.4.1. Surface Accuracy Evaluation

#### 3.4.2. Structural Column Accuracy Evaluation

_{m}is the true coordinates of the structural column corner points and P

_{a}is the measured coordinates of the same corner point after registration. The ADD is used to reflect the deviation of the angle between the corner points of the structure columns, defined as the angular distance between the corner points of the wall and the referenced column in BIM. As shown in Figure 7, the result of coarse registration is represented by the superposition of two boxes; the blue box and red box represent BIM and point cloud, respectively.

#### 3.4.3. Statistical Analysis and Visualization of Deviation Results

## 4. Case Study

#### 4.1. Construction Site Data Collection and Preprocessing

^{8}points, and the average density of the point cloud is 5316 pts/m

^{2}, which includes richly detailed characteristics and clearly shows the internal components. The data show that the density of the point cloud data of the subway station is high enough to accurately represent the geometric information of each facade, slab, and structural column in the subway station. Figure 10b shows the BIM model of the subway station. The BIM is created in the design stage, and the interior of the model includes some typical structures, i.e., facades, slabs (top and bottom slabs), and structural columns.

#### 4.2. Point Cloud and BIM Registration

_{1}, the rigid transformation is calculated based on the poses of the BIM grid center and the virtual grid center. Figure 11 shows the registration result of the point cloud slice and the BIM grid, resulting in the approximate alignment of the BIM with the point cloud model. However, it is challenging to meet the evaluation requirements of geometric accuracy. Figure 12 (enlarged area) shows that there are still obvious gaps in the areas on both sides of the subway station (A-2 and C-38). Therefore, fine registration is used to further improve the registration accuracy. The inner wall lines are extracted from the BIM, and the transformation matrix M

_{2}is obtained after the point cloud is finely registered with the inner wall lines using the PL-ICP method. The initial point cloud coordinate is transformed using $M={M}_{2}\cdot {M}_{1}$ to obtain the final point cloud model. The inverse transformation of the aforesaid transformation is the coordinate transformation from the BIM to the point cloud model. Figure 13 shows the result of fine registration from the point cloud model to the BIM. The average deviation value is 17.8 ± 0.94 mm, and the fine registration result distributes the deviation evenly on the inner wall lines. The coarse-to-fine registration of the point cloud achieves centimeter-level registration accuracy, which provides reliable results for further geometric accuracy evaluation.

#### 4.3. Point Cloud Structure Element Extraction

_{th}is set to 15° and 30 nearest neighbors were used (k = 30); the residual threshold r

_{th}is calculated by the 98th percentile of the plane fitting residuals. The results of the structural element extraction of the subway station are shown in Figure 14, where each surface is distinguished by a different color, and corresponding features of the interior of the station are obtained, including 4 facades, 2 slabs, and 50 structural columns. Table 1 shows the results of the quantitative analysis of the structural elements of the point cloud; the point cloud is dense enough to accurately display the geometric characteristics of the components. Then, all the structural elements extracted are evaluated in order according to the method proposed in this paper.

#### 4.4. Surface Accuracy Evaluation

#### 4.4.1. Facade Evaluation

#### 4.4.2. Evaluation of the Top and Bottom Slabs

#### 4.5. Structural Column Accuracy Evaluation

## 5. Discussion

## 6. Conclusions

^{2}. The successful application in the Hongqi Road subway station demonstrates the potential of this proposed method. It can be applied to other comparable applications.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Abbreviation
| Nomenclature |

3D | Three-dimensional |

BIM | Building Information Modeling |

AEC | Architecture, Engineering, and Construction |

2D | Two-dimensional |

GNSS | Global Navigation Satellite System |

ICP | Iterative Closest Point |

RANSAC | Random Sample Consistency |

PCA | Principal Component Analysis |

E | Genetic Algorithm |

ANN | Artificial Neural Network |

CWT | Continuous Wavelet Transform |

PL-ICP | Point-to-line Iterative Closest Point |

KD tree | K-Dimensional tree |

PDM | Plane Discrepancy Metric |

SCDM | Structural Column Discrepancy Metric |

ADD | Angular Distance Deviation |

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**Figure 1.**(

**a**) Workflow of geometric accuracy evaluation using 3D laser scanning; (

**b**) data processing method.

**Figure 4.**Principle of the PL-ICP algorithm, aiming at minimizing the sum of squared distances between the target point and the line segment that connects two adjacent points.

**Figure 10.**(

**a**) Scanning point cloud of the subway station; (

**b**) the design BIM of the subway station.

**Figure 16.**Evaluation of east facade: (

**a**) deviation distance accuracy visualization result; (

**b**) histogram of the error distribution.

**Figure 17.**Evaluation of west facade: (

**a**) deviation distance accuracy visualization result; (

**b**) histogram of the error distribution.

**Figure 18.**Evaluation of north facade: (

**a**) deviation distance accuracy visualization result; (

**b**) histogram of the error distribution.

**Figure 19.**Evaluation of south facade: (

**a**) deviation distance accuracy visualization result; (

**b**) histogram of the error distribution.

**Figure 20.**Roof slab: (

**a**) deviation distance accuracy visualization result; (

**b**) histogram of the error distribution.

**Figure 21.**Base slab: (

**a**) deviation distance accuracy visualization result; (

**b**) histogram of the error distribution.

**Figure 22.**(

**a**) Visualization results of the 3D deviation of structural columns; (

**b**) histogram of the error distribution of the structural columns.

**Figure 23.**Structural column C-2: (

**a**) 3D deviation visualization results; (

**b**) error distribution histogram.

**Figure 24.**Structural column B-18: (

**a**) 3D deviation visualization results; (

**b**) error distribution histogram.

**Figure 25.**Structural column B-35: (

**a**) 3D deviation visualization results; (

**b**) error distribution histogram.

**Figure 26.**Results of the structural column accuracy evaluation: (

**a**) SCDM of structural column corner points; (

**b**) ADD of structural column corner points.

**Figure 27.**Measured point cloud of structure column A-2. A red curtain was wrapped around the perimeter of structural column A-2.

Structural Element | Number of Points | Point Density (pts/m^{2}) |
---|---|---|

East facade | 755,424 | 5502 |

West facade | 902,986 | 4386 |

North facade | 15,022,981 | 6351 |

South facade | 14,858,647 | 6533 |

Roof slab | 19,793,397 | 5182 |

Base slab | 6,799,713 | 3742 |

Structural column | 2,252,290 | 5513 |

**Table 2.**A display of columns in the point cloud and BIM that exceed or do not exceed the tolerance.

Exceed Tolerance | Not Exceed Tolerance | ||
---|---|---|---|

C-2 | A-2 | A-4 | C-12 |

B-35 | B-36 | A-12 | A-13 |

B-34 | C-6 | B-15 | B-17 |

A-5 | A-7 | B-20 | B-32 |

Structural Column | SCDM (mm) | ADD (°) |
---|---|---|

A-2 | 80.5 | 1.55 |

C-2 | 72.6 | 0.39 |

B-36 | 50.9 | 0.19 |

B-35 | 48.1 | 0.36 |

B-34 | 38.3 | 0.64 |

C-6 | 36.6 | 0.41 |

A-5 | 36.6 | 0.39 |

A-7 | 32.8 | 0.94 |

C-13 | 32.1 | 0.65 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Q.; Qian, P.; Liu, Y.; Li, T.; Yang, L.; Yang, F.
Geometric Accuracy Evaluation Method for Subway Stations Based on 3D Laser Scanning. *Appl. Sci.* **2022**, *12*, 9535.
https://doi.org/10.3390/app12199535

**AMA Style**

Wang Q, Qian P, Liu Y, Li T, Yang L, Yang F.
Geometric Accuracy Evaluation Method for Subway Stations Based on 3D Laser Scanning. *Applied Sciences*. 2022; 12(19):9535.
https://doi.org/10.3390/app12199535

**Chicago/Turabian Style**

Wang, Quankai, Peng Qian, Yunping Liu, Tao Li, Lei Yang, and Fan Yang.
2022. "Geometric Accuracy Evaluation Method for Subway Stations Based on 3D Laser Scanning" *Applied Sciences* 12, no. 19: 9535.
https://doi.org/10.3390/app12199535