# Point Cloud-Based Smart Building Acceptance System for Surface Quality Evaluation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{a}, L

_{b}perpendicular to each other, with one of them (L

_{a}) parallel to the shorter wall of the testing room. Then the distance between L

_{b}from the longer wall is measured as d

_{i}, and the range, R, is calculated as the squareness as Equation (1) says. The general tolerance of the above three indicators from different codes are summarized in Table 1.

## 2. Related Works

#### 2.1. SQE Using PCD

^{2}. Meanwhile, there are several commercial software packages that enable squareness evaluation based on PCD, e.g., FARO, StructionSite, etc., but all of them are semi-automatic, which requires manual operation by choosing the suitable program and data.

#### 2.2. Surface Segmentation and Fitting

## 3. System Framework

- Data preparation. The PCD acquisition parameters and corresponding scanning modes are discussed by gathering the data from the literature and testing the scanner with different modes in the laboratory, in order to ensure the data quality. Then the dense PCD is registered and reduced for computational efficiency.
- Surface segmentation and plane fitting. An improved DBSCAN algorithm is introduced in this study to segment various surfaces accurately by introducing the additional processes of plane validation and coplanar parameter. Moreover, a slide window-based sampling method is applied to obtain the sample PCD for SQE. Then a revised Least Squares Method (LSM) algorithm is proposed to remove the outliers and obtain the best-fitted reference plane for the later processes.
- Automated SQE and result visualization. The flatness, verticality, and squareness evaluation are performed based on the reference plane, and a color-coded map is produced for a clear visualization.

#### 3.1. Data Preparation

#### 3.2. Surface Segmentation and Plane Fitting

#### 3.2.1. Surface Segmentation Based on Improved DBSCAN

**Labeling of the points.**Within the proposed method, the first step is to identify all the core points and label them, which is similar to the conventional DBSCAN. This is to prepare the input of the next step, for facilitating the sample points selection.

**Sample points selection and plane fitting.**This step is to select three potential points from the core points set to fit an initial plane. Apparently, the potential points should be the core point away from the intersections and boundaries of the PCD. The selection process is conducted as follows. Firstly, a core point c

_{i}within the test core point group and its k-nearest neighbors p

_{ij}(j = 1, 2, … k) are input to initiate the process, and the distance matrix $dis{t}_{i}$ is calculated within the group. And then the three farthest away points, (e.g., ${p}_{ik},{p}_{ik-1},{p}_{ik-2},$), are selected as the potential candidate points based on the distance matrix. Next, the normal directional compatibility check needs to be conducted according to the following requirement:

_{i}and potential points ${p}_{il},{p}_{il+1},{p}_{il+2}$, respectively, and ${\overline{n}}_{{}_{{p}_{ij}}}$ denotes the normal vector of the j-th k-nearest neighbors. By doing the above check, it can ensure that the normal directions of the three selected points are essentially compatible with the average normal direction of all points in this k-neighborhood.

**Plane validation.**It is clear that the fitted plane based on the three core points selected above should have as small a distance as possible from the nearby points within the entire sample. Therefore, the plane validation is proposed here to verify the validity of the fitted plane.

_{1}< r

_{2}, the further process can be conducted based on the plane F, where ${r}_{1}=card\left\{{d}_{m}|{d}_{m}\ge \mu +\sigma \right\}(m=0,1,\dots k)$, and ${r}_{2}=0.25(k-2)$.

**Clustering.**Once a satisfied fitting plane P and the corresponding core point ${c}_{i}$ are determined, the clustering is able to be conducted based on the DBSCAN and a coplanar parameter, $\lambda $. If the point m of the multi-plane PCD is in the same cluster with core point ${c}_{i}$, two requirements should be satisfied: (1) the point m is density-reachable of ${c}_{i}$ according to the theory of DBSCAN; and (2) the distance between point m to plane P is less than the coplanar parameter $\lambda $, while $\lambda $ is defined as follows:

#### 3.2.2. Plane Fitting

**Step 1**: The testing surface sample PCD $P=\left\{{P}_{i}|{P}_{i}={[{x}_{i},{y}_{i},{z}_{i}]}^{T}\right\}$ is input and the initial parameters, w, p, n, q, are determined according to the following formulas based on LMedS:

**Step 2.**Extract a subsample $N=\left\{{N}_{i}|{N}_{i}\in P,i=1,2,\dots n\right\}$ from P, and fit a plane A, a’x + b’y + c’z + d’ = 0, by means of the PCA method. Then the median of the residuals of the Euclidean distance of each point in subsample N from the fitted plane A is determined, denoted by ${M}_{N}=\mathrm{med}{d}_{i}({N}_{i},A),i=1,2,\dots n$.

**Step 3.**Repeat steps 2–3 until the number of iterations is reached to k, record the set of the median value $M=\left\{{M}_{i}{|{M}_{i}=[{M}_{1},{M}_{2},\dots ,{M}_{k}]}^{T}\right\},i=1,2,\dots k$, from which find out the minimum value, denoted by ${M}_{M}$. Afterwards, the robust standard deviation $\sigma $ and weight ${w}_{i}$ are determined to segment the outliers and inliers for the sample as Equations (7) and (8) say, and the final plane, F: ax + by + cz + d = 0, is fitted based on the segmented PCD.

_{i}indicates the Euclidean distance of point P

_{i}in sample P, and ${w}_{i}$ means the weight for point ${P}_{i}$ in sample P.

#### 3.3. SQE Based on PCD

#### 3.3.1. Flatness Evaluation (FE)

#### 3.3.2. Verticality Evaluation (VE)

#### 3.3.3. Squareness Evaluation (SE)

## 4. Experiment Validation

#### 4.1. Data Collection and Pre-Processing of PCD

^{9}points are imported into the software “Cyclone REGISTER 360”, which automatically registers the data by searching the target balls in the separated PCDs. It should be noticed that the coordinates of the PCD should be transferred.

^{7}points in total as shown in Figure 12b.

#### 4.2. Surface Segmentation

#### 4.3. Automatic SQE Results

#### 4.3.1. Flatness Evaluation Results

#### 4.3.2. Verticality and Squareness Evaluation Results

^{2}in size, making it more difficult for the formwork and therefore prone to this problem.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Definition of verticality assessment: (

**a**) horizontal deviation method, (

**b**) angle method, and (

**c**) flatness assessment of concrete surface. (Redrawn from [6]).

**Figure 12.**Segmentation results of the test PCD: (

**a**) scanning on-site, (

**b**) PCD after registration and denoising, (

**c**) PCD after clustering by room, and (

**d**) detailed view of PCD after clustering by room.

**Figure 14.**Evaluation metrics of surface segmentation on Room 1 and Room 2; (

**a**) P, (

**b**) R, and (

**c**) F1.

**Figure 16.**Flatness evaluation results of (

**a**) top-right view, (

**b**) bottom-left view, (

**c**) ceiling, and (

**d**) floor.

**Figure 18.**Squareness evaluation results of the tested apartment: (

**a**) top view and (

**b**) detailed view of Room 3 and Room 4.

Category | GB 50204-2015 [6] | PCI MNL-135 [8] | ACI-ITG-7M [9] | EN 13670 [10] | |
---|---|---|---|---|---|

Verticality [mm] | Structural column/wall | 5 (H ≤ 6000); | 5/2400 | 6/3000 | 25 |

10 (H > 6000) | |||||

Non-structural column | 2 | 5/2400 | 6/3000 | 25 | |

Flatness [mm] | - | 8 | 6/3000 | ±1/8 in. per 10 ft ±1/2 in. maximum | 9/2000 (Molded surface) |

15/2000 (Not molded surface) | |||||

Squareness [mm] | - | 10/2000 | - | ±1/8 in. per 6 ft, ±1/2 in. maximum | - |

Scanning Mode | Maximum Range (m) | Resolution (mm) | Scanning Time (min) |
---|---|---|---|

1 | 2 | 0.4 | 13 |

2 | 10 | 0.4 | 18 |

3 | 20 | 0.4 | 25 |

4 | 40 | 0.4 | 38 |

5 | 80 | 0.4 | 63 |

6 | 120 | 0.4 | 88 |

7 | 2 | 0.8 | 10 |

8 | 10 | 0.8 | 11 |

9 | 20 | 0.8 | 18 |

10 | 40 | 0.8 | 25 |

11 | 80 | 0.8 | 39 |

12 | 120 | 0.8 | 54 |

13 | 2 | 1.6 | 2 |

14 | 10 | 1.6 | 3 |

15 | 20 | 1.6 | 4 |

16 | 40 | 1.6 | 6 |

17 | 80 | 1.6 | 10 |

18 | 120 | 1.6 | 13 |

LSM | RANSAC | Proposed Method | ||
---|---|---|---|---|

Without Gaussian noise | a | 0.4082 | 0.4082 | 0.4082 |

b | 0.8165 | 0.8165 | 0.8165 | |

c | −0.4082 | −0.4082 | −0.4082 | |

d | 0.4082 | 0.4082 | 0.4082 | |

δ | 2.3075 × 10^{−14} | 4.0058 × 10^{−16} | 1.8998 × 10^{−16} | |

With Gaussian noise | a | 0.4230 | 0.4121 | 0.4080 |

b | 0.8105 | 0.8186 | 0.8165 | |

c | −0.4053 | −0.4001 | −0.4085 | |

d | 0.3683 | 0.3414 | 0.4109 | |

δ | 0.3112 | 0.0810 | 0.0201 |

Plane Name | A | B | C | D | δ | Max. dist/m | Satisfaction Rate/% |
---|---|---|---|---|---|---|---|

Ceiling | 0.0009 | −0.0008 | 1.0000 | −1.5069 | 2.54 × 10^{−3} | 0.0216 | 95.36 |

Floor | 0.0003 | −0.0011 | 1.0000 | 1.3322 | 2.87 × 10^{−3} | 0.0552 | 89.21 |

Wall 1 | 0.0013 | 1.0000 | 0.0006 | −4.8684 | 5.58 × 10^{−4} | 0.0059 | 99.96 |

Wall 2 | −1.0000 | 0.0010 | 0.0000 | −6.1567 | 6.84 × 10^{−4} | 0.0013 | 99.95 |

Wall 3 | −0.0010 | −1.0000 | 0.0005 | 1.6980 | 4.75 × 10^{−4} | 0.0066 | 99.94 |

Wall 4 | −1.0000 | −0.0003 | −0.0007 | −0.7066 | 2.94 × 10^{−4} | 0.0087 | 99.95 |

Wall 5 | −1.0000 | 0.0004 | −0.0007 | 1.1170 | 5.01 × 10^{−4} | 0.0098 | 99.98 |

Room Number | Wall Number | Theta/Degree | L/mm |
---|---|---|---|

Room 1 | wall 1 | 90.0201 | 0.9946 |

wall 2 | 90.0116 | 0.5764 | |

wall 3 | 90.0499 | 2.4743 | |

wall 4 | 89.9983 | 0.0859 | |

wall 5 | 89.9653 | 1.7236 | |

Room 2 | wall 1 | 90.0248 | 1.2280 |

wall 2 | 90.0173 | 0.8593 | |

wall 3 | 89.9131 | 4.3092 | |

wall 4 | 90.0591 | 2.9291 | |

wall 5 | 90.0588 | 2.9174 | |

Room 3 | wall 1 | 90.1174 | 5.8240 |

wall 2 | 90.3253 | 16.1374 | |

wall 3 | 90.1381 | 6.8517 | |

wall 4 | 90.1232 | 6.1122 | |

wall 5 | 90.3229 | 16.0185 | |

wall 6 | 89.6756 | 16.0912 | |

wall 7 | 89.6281 | 18.4488 | |

Room 4 | wall 1 | 90.6448 | 31.9839 |

wall 2 | 90.0113 | 0.5623 | |

wall 3 | 89.2573 | 36.8408 | |

wall 4 | 89.9903 | 0.4800 | |

Room 5 | wall 1 | 90.0458 | 2.2723 |

wall 2 | 89.9416 | 2.8953 | |

wall 3 | 90.0435 | 2.1591 | |

Room 6 | wall 1 | 90.0999 | 4.9559 |

wall 2 | 90.0420 | 2.0833 | |

wall 3 | 90.0262 | 1.2977 | |

wall 4 | 90.0227 | 1.1254 | |

Room 7 | wall 1 | 89.8022 | 9.8097 |

wall 2 | 89.9969 | 0.1530 | |

wall 3 | 89.7262 | 13.5829 | |

wall 4 | 89.9337 | 3.2863 |

Room Number | Wall Number | Squareness | |
---|---|---|---|

Radian | Degree | ||

Room 1 | wall 1, wall 2 | 1.5712 | 90.0215 |

wall 2, wall 3 | 1.5704 | 89.9758 | |

wall 3, wall 4 | 1.5717 | 90.0530 | |

wall 5, wall 1 | 1.5680 | 89.8395 | |

Room 2 | wall 1, wall 2 | 1.5705 | 89.9825 |

wall 2, wall 3 | 1.5708 | 90.0019 | |

wall 3, wall 4 | 1.5721 | 90.0720 | |

wall 5, wall 1 | 1.5699 | 89.9481 | |

Room 3 | wall 1, wall 2 | 1.5697 | 89.9347 |

wall 2, wall 3 | 1.5725 | 90.0982 | |

wall 4, wall 5 | 1.5708 | 89.9991 | |

wall 5, wall 6 | 1.5603 | 89.3998 | |

wall 6, wall 7 | 1.5668 | 89.7729 | |

wall 7, wall 1 | 1.5852 | 90.8271 | |

Room 4 | wall 1, wall 2 | 1.5702 | 89.9665 |

wall 2, wall 3 | 1.5773 | 90.3717 | |

wall 3, wall 4 | 1.5763 | 90.3148 | |

wall 4, wall 1 | 1.5712 | 90.0235 | |

Room 5 | wall 1, wall 2 | 1.5704 | 89.9795 |

wal2, wall 3 | 1.5704 | 89.9789 | |

Room 6 | wall 1, wall 2 | 1.5724 | 90.0904 |

wall 2, wall 3 | 1.5709 | 90.0085 | |

wall 3, wall 4 | 1.5704 | 89.9784 | |

wall 4, wall 1 | 1.5718 | 90.0603 | |

Room 7 | wall 1, wall 2 | 1.5687 | 89.8787 |

wall 2, wall 3 | 1.5703 | 89.9695 | |

wall 3, wall 4 | 1.5707 | 89.9938 | |

wall 4, wall 1 | 1.5723 | 90.0845 |

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## Share and Cite

**MDPI and ACS Style**

Cai, D.; Chai, S.; Wei, M.; Wu, H.; Shen, N.; Zhou, Y.; Ding, Y.; Hu, K.; Hu, X.
Point Cloud-Based Smart Building Acceptance System for Surface Quality Evaluation. *Buildings* **2023**, *13*, 2893.
https://doi.org/10.3390/buildings13112893

**AMA Style**

Cai D, Chai S, Wei M, Wu H, Shen N, Zhou Y, Ding Y, Hu K, Hu X.
Point Cloud-Based Smart Building Acceptance System for Surface Quality Evaluation. *Buildings*. 2023; 13(11):2893.
https://doi.org/10.3390/buildings13112893

**Chicago/Turabian Style**

Cai, Dongbo, Shaoqiang Chai, Mingzhuan Wei, Hui Wu, Nan Shen, Yin Zhou, Yanchao Ding, Kaixin Hu, and Xingyi Hu.
2023. "Point Cloud-Based Smart Building Acceptance System for Surface Quality Evaluation" *Buildings* 13, no. 11: 2893.
https://doi.org/10.3390/buildings13112893