# Three-Dimensional Reconstruction of Building Roofs from Airborne LiDAR Data Based on a Layer Connection and Smoothness Strategy

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Extraction of Building Rooftop Points

#### 2.2. Smoothness-Oriented Rooftop Patch Segmentation

#### 2.2.1. Rooftop Patch Segmentation

#### 2.2.2. Smoothness-Oriented Rooftop Patch Optimization

#### 2.3. Generation of Layer-Connection Points

#### 2.3.1. Construction of the 2-D Grid System

_{min}, y

_{min}) represents the minimum coordinates of the building points, and Gridsize represents the size of a grid cell.

#### 2.3.2. Calculation of Layer-Connection Points

#### 2.3.3. Optimization of Layer-Connection Points

#### 2.4. Building Model Reconstruction

#### 2.5. Sensitivity Analysis of the Key Parameters

_{w}and the height difference T

_{h}were set according to the data source, and these values usually refer to the length of the largest building (106 m) and the height of the lowest building (3 m) in the experimental area, respectively. The fixed step length L

_{c}, and roughness value R

_{v}were, respectively, set to 3 m and 0.8 m, empirically. Two sets of different values (in meters) were tested while setting the values for the two parameters L

_{c}and R

_{v}. For L

_{c}the test values were 1, 3, 5, 7 m; for R

_{v}the test values were 0.4, 0.6, 0.8, 1.0, and 1.2 m. According to the completeness and correctness of the segmented rooftop patches, we found that the smaller L

_{c}and the larger R

_{v}could lead to that the extracted building point clouds contained some tree LiDAR points. Conversely, there could be some missing building points if L

_{c}was too large and R

_{v}was too small. The optimal extraction results were observed at L

_{c}= 3 m and R

_{v}= 0.8 m.

_{s}and the number of inner points N are related to the input LiDAR data. To guarantee that there were more than ten points to calculate the normal of each LiDAR point, R

_{s}is suitable for 2–3 times average of point spacing. Elaborate consideration was given to the value of N as follows. We assumed that the area of a minimum rooftop patch that could be detected was 4 m

^{2}, i.e., 2 m × 2 m. According to the point density of LiDAR data, a threshold for N can then be calculated easily. The distance threshold T

_{d}were set to 0.2, 0.3, 0.4, 0.5, and 0.6 m to find the optimal value. In the process of patch optimization, the phenomenon of over-smoothing will be occurred, if T

_{d}is set too large. At T

_{d}= 0.5 m the effect of smoothing is moderate. The probability is a minimum probability of finding at least one good set of observations in all iterative procedures. It usually lies between 0.90 and 0.99. In our experiments, the probability was set to 0.98. During the generation of layer-connection points, a grid-based method is introduced, and the cell size is set empirically.

## 3. Experiments and Analysis

#### 3.1. Experimental Data

^{2}, its average point spacing is about 0.25 m, and data had a vertical accuracy of 0.15 m and a horizontal accuracy of 0.20 m. We used the campus of Nanjing University, China, as the experimental Region 1 (Figure 6); this region covered an area of about 900 m × 500 m and contained 4.2 million LiDAR points. Figure 6a,b shows the aerial orthophotos with 0.3 m resolution and the LiDAR data from a side view, respectively. Figure 6c shows no-data areas where very sparse LiDAR points (one point in 30 m

^{2}) were collected as a result of the particular color and special structures of the corresponding building tops. The buildings in these no-data areas were not involved in the 3-D reconstruction process. The experimental Region 2 (Figure 7) was a residential area in the Jianye district, Nanjing City, China; this region covered an area of about 900 m × 600 m and contained 4.5 million LiDAR points. Figure 7a,b shows the aerial orthophotos and the LiDAR data, respectively. There were many buildings with various sizes and spatial distributions in Region 2.

#### 3.2. Experimental Results

#### 3.3. Experimental Analysis

#### 3.3.1. Correctness and Completeness

#### 3.3.2. Deviation Analysis of the Reconstructed Building Roofs

_{i}from reference data R and searched for the most neighboring triangular polygon M

_{i}by using a method that has been described previously in the literature [47]. Then, the deviation distance between each LiDAR point and its corresponding patch was calculated. The statistical results of the deviation distances for Regions 1 and 2 were computed based on the validation point set (as shown in Figure 10a,b).

#### 3.3.3. Influence of Elevation to 3-D Roof Reconstruction

#### 3.4. Experimental Discussion

#### 3.4.1. Evaluation from the ISPRS Test Project

^{2}were 75.5% and 99.0%, respectively. For Area 2, the completeness and the correctness of the extracted roof planes by using the proposed method were 71.0% and 100.0%, respectively; the completeness and the correctness of the roof planes covering an area of at least 10 m

^{2}were 89.6% and 100.0%, respectively. For Area 3, the completeness and the correctness of the extracted roof planes were 74.9% and 100.0%, respectively; the completeness and the correctness of the roof planes covering an area of at least 10 m

^{2}were 85.5% and 100.0%, respectively. Although there was a clear difference between the quality metrics for all planes and for roof planes larger than 10 m

^{2}, the reconstruction quality of the proposed method could reach about or above the average accuracy of the six state-of-the-art methods. In addition, the geometrical errors (RMS, RMSZ) caused by the proposed approach were also in the range of the six previous methods. Therefore, the proposed method produced a good reconstructions for Areas 1–3.

#### 3.4.2. Comparison with other Methods

^{2}in this paper) as replacement data. First, the roughness, i.e., standard deviation, needs to be calculated for each point p. In the process of determining roughness, the neighboring points (20 points in this paper) of point p are defined. Then, the roughness of point p can be determined based on Euclidean distances from all neighboring points to the fitted plane. Finally, the roughness of each building can be derived according to the calculated roughness of each point.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Smoothing of building rooftop points: (

**a**) original points; (

**b**) segmented points; and (

**c**) smoothed points.

**Figure 2.**An example of layer-connection points: (

**a**) yellow points represent the first layer (ground), blue points represent the second layer, and red points represent the third layer; (

**b**) an enlarged view; (

**c**); (

**d**) lines to connect points from two layers; and (

**e**) line to connect points from three layers.

**Figure 3.**Example of merging rooftop patches into a layer. (

**a**) Points with different colors represent different rooftop patches; the blue line represents the intersection line between S1 and S2; and (

**b**) red points and blue points represent a roof layer.

**Figure 4.**Calculation of layer-connection points, points with different colors representing different roof layers, and the blue rectangle representing the x–y coordinates of the derived layer-connection point: (

**a**) the points inside the five cells belonging to the same roof layer; and (

**b**), (

**c**), (

**d**), (

**e**) the points inside the five cells belonging to different roof layers.

**Figure 5.**An example of building model reconstruction: (

**a**) layer-connection points; (

**b**) rooftop construction; and (

**c**) wall construction.

**Figure 6.**Experimental Region 1: (

**a**) aerial orthophotos with 0.3 m resolution (no-data areas are shown by yellow boxes); (

**b**) airborne LiDAR data; and(

**c**) no-data areas (black), corresponding the yellow boxes in (

**a**) with letters.

**Figure 7.**Experimental Region 2: (

**a**) aerial orthophotos with 0.3 m resolution; and (

**b**) airborne LiDAR data.

**Figure 8.**Reconstruction results in Region 1: (

**a**) an overview; (

**b**) a side view of the local reconstructed roof models; and (

**c**) and (

**d**), building roof models for the red box in (

**b**).

**Figure 9.**Reconstruction results in Region 2: (

**a**) an overview; (

**b**) a side view of the local reconstructed roof models; and (

**c**) and (

**d**), building roof models for the red box in (

**b**).

**Figure 10.**Deviation distances between the reconstructed building roof models and the LiDAR-derived validation data, as represented by points with different colors: (

**a**), (

**b**) Region 1 and Region 2, respectively.

**Figure 11.**Evaluation of the building roofs’ deviations under different elevations, where the solid squares in the figures represent the average values of the deviation distances under each elevation range, and the error bars represent the positive and negative deviations of each average value: (

**a**), (

**b**) Region 1 and Region 2, respectively.

**Figure 12.**Comparison of Approaches (abbreviated as App.) A, B, and C: (

**a**), (

**b**), and (

**c**) the reconstructed roof models of Buildings 1, 2, and 3, respectively.

**Figure 13.**Comparison of Approaches (abbreviated as App.) A, B, and C: (

**a**), (

**b**), and (

**c**) The reconstructed roof models of Buildings 4, 5, and 6, respectively.

**Figure 14.**Roughness comparison between Approaches A and B: (

**a**), (

**c**) roughness of roof models reconstructed using Approach A for Buildings 4 and 6; (

**b**), (

**d**) roughness of roof models reconstructed using Approach B for Buildings 4 and 6, respectively. Data are represented by points with different colors.

Procedure | Threshold | Scale | Setting Basis | |
---|---|---|---|---|

Extraction of building rooftop points | Initial window I_{w} | The length of the largest building | Data source | |

Fixed step length L_{c} | 3 m | Empirical | ||

Height difference T_{h} | The minimum building height | Data source | ||

Roughness value R_{v} | 0.8 m | Empirical | ||

Smoothness-oriented rooftop patch segmentation | Patch segmentation | Search radius R_{s} | 2–3 times average of point spacing | Empirical |

Patch optimization | Distance threshold T_{d} | 0.5 m | Empirical | |

Number of inner points N | 2 × 2 × point density | Empirical | ||

Probability P | 0.98 | Empirical | ||

Generation of layer-connection points | Construction of the 2-D grid system | Cell size C | 2–3 times average of point spacing | Empirical |

Reconstructed Results | Correct Quantity | Missing Quantity | False Quantity | Completeness (%) | Correctness (%) | |||||
---|---|---|---|---|---|---|---|---|---|---|

Number | Area (m^{2}) | Number | Area (m^{2}) | Number | Area (m^{2}) | Number | Area | Number | Area | |

Region 1 | 236 | 84,183.25 | 28 | 8695.64 | 7 | 2432.90 | 89.39 | 90.64 | 97.12 | 97.19 |

Region 2 | 1145 | 145,659.82 | 122 | 12,924.63 | 55 | 10,526.89 | 90.37 | 91.85 | 95.42 | 93.26 |

Reconstructed Results | Number of Points | Maximum | Average | Std. Dev. | Skewness | Kurtosis | Percentage of Less Than 0.3 m (%) |
---|---|---|---|---|---|---|---|

Region 1 | 743,502 | 3.53 | 0.05 | 0.18 | 4.78 | 31.47 | 96.61 |

Region 2 | 1,672,006 | 4.15 | 0.12 | 0.25 | 4.28 | 34.92 | 93.28 |

**Table 4.**Overview of the reconstruction methods. ID: Identifier of the method used in this paper. Researcher/Affiliation: name and affiliation of the person submitting the results. Reference: a reference where the method is described.

ID | Researcher | Affiliation | Reference |
---|---|---|---|

CKU | J.-Y. Rau | N. Cheng-Kung U., Taiwan | (Rau and Lin, 2011) |

ITCE1 | S. Oude Elberink | ITC, The Netherlands | (Oude Elberink and Vosselman, 2009) |

ITCE2 | S. Oude Elberink | ITC, The Netherlands | (Oude Elberink and Vosselman, 2009) |

ITCX | B. Xiong | ITC, The Netherlands | (Xiong et al., 2014) |

VSK | P. Dorninger | TU Vienna, Austria | (Dorninger and Pfeifer, 2008) |

YOR | G. Sohn | York University, Canada | (Sohn et al., 2008) |

NUC | Y.J. Wang | Nanjing University, China | This paper |

**Table 5.**Evaluation of building reconstruction results in Areas 1, 2, and 3. The best values per column are printed in bold font.

ID | Cm_{ob}/Cr_{ob} [%] | Cm_{10}/Cr_{10} [%] | N_{1:M}/N_{N:1}/N_{N:M} | RMS [m] | RMSZ [m] |
---|---|---|---|---|---|

Area 1 (288 roof planes) | |||||

CKU | 86.7/98.9 | 86.7/99.3 | 10/36/3 | 0.66 | 0.70 |

ITCE1 | 60.8/94.6 | 58.5/94.0 | 16/26/17 | 0.91 | 0.55 |

ITCE2 | 65.3/97.3 | 63.3/97.3 | 0/38/3 | 0.94 | 0.55 |

ITCX | 76.0/94.5 | 72.9/95.1 | 2/40/2 | 0.84 | 0.53 |

VSK | 72.2/96.7 | 77.7/96.5 | 7/42/6 | 0.79 | 0.65 |

YOR | 88.2/98.5 | 89.9/98.2 | 5/36/14 | 0.75 | 0.58 |

NUC | 73.6/99.2 | 75.5/99.0 | 2/42/3 | 0.92 | 0.45 |

Area 2 (69 roof planes) | |||||

CKU | 78.3/93.1 | 90.0/93.7 | 8/4/0 | 0.85 | 1.02 |

ITCE1 | 79.7/73.7 | 94.0/73.7 | 0/7/0 | 1.11 | 3.33 |

ITCE2 | 79.7/95.0 | 94.0/100.0 | 0/7/0 | 1.16 | 3.31 |

ITCX | 62.3/92.9 | 74.0/92.7 | 2/4/0 | 0.79 | 0.44 |

VSK | 73.9/100.0 | 88.0/100.0 | 3/5/1 | 1.03 | 0.88 |

YOR | 73.9/100.0 | 90.0/100.0 | 5/3/0 | 0.77 | 1.04 |

NUC | 71.0/100.0 | 89.6/100.0 | 3/7/1 | 0.83 | 0.62 |

Area 3 (235 roof planes) | |||||

CKU | 81.3/98.4 | 82.2/98.3 | 4/48/2 | 0.76 | 0.65 |

ITCE1 | 67.7/100.0 | 62.8/100.0 | 0/47/2 | 0.96 | 0.29 |

ITCE2 | 64.3/100.0 | 55.9/100.0 | 0/46/0 | 1.04 | 0.42 |

ITCX | 70.2/100.0 | 62.8/100.0 | 1/48/0 | 0.87 | 0.30 |

VSK | 76.6/99.1 | 74.5/99.1 | 3/50/0 | 0.84 | 0.38 |

YOR | 84.7/100.0 | 89.0/100.0 | 2/51/1 | 0.77 | 0.35 |

NUC | 74.9/100.0 | 85.5/100.0 | 0/49/0 | 0.91 | 0.36 |

**Table 6.**Comparison of deviation distances for Buildings 1–6 reconstructed by Approaches A, B, and C.

Reconstructed Results | Number of Points | Approach A | Approach B | Approach C | |||
---|---|---|---|---|---|---|---|

Average | Std. Dev. | Average | Std. Dev. | Average | Std. Dev. | ||

Building 1 | 15,163 | 0.02 | 0.11 | 0.03 | 0.13 | 0.28 | 0.56 |

Building 2 | 29,480 | 0.06 | 0.18 | 0.09 | 0.19 | 0.10 | 0.27 |

Building 3 | 23,838 | 0.08 | 0.25 | 0.19 | 0.25 | 0.21 | 0.35 |

Building 4 | 28,151 | 0.14 | 0.22 | 0.17 | 0.23 | 0.15 | 0.29 |

Building 5 | 17,612 | 0.05 | 0.16 | 0.12 | 0.31 | 0.06 | 0.17 |

Building 6 | 18,705 | 0.07 | 0.13 | 0.13 | 0.14 | 0.13 | 0.22 |

Reconstructed Buildings | Number of Rooftop Patches | Approach A | Approach B |
---|---|---|---|

Building 1 | 5 | 0.006 | 0.009 |

Building 2 | 13 | 0.004 | 0.128 |

Building 3 | 14 | 0.004 | 0.237 |

Building 4 | 4 | 0.005 | 0.221 |

Building 5 | 5 | 0.005 | 0.189 |

Building 6 | 3 | 0.002 | 0.171 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Xu, H.; Cheng, L.; Li, M.; Wang, Y.; Xia, N.; Chen, Y.; Tang, Y.
Three-Dimensional Reconstruction of Building Roofs from Airborne LiDAR Data Based on a Layer Connection and Smoothness Strategy. *Remote Sens.* **2016**, *8*, 415.
https://doi.org/10.3390/rs8050415

**AMA Style**

Wang Y, Xu H, Cheng L, Li M, Wang Y, Xia N, Chen Y, Tang Y.
Three-Dimensional Reconstruction of Building Roofs from Airborne LiDAR Data Based on a Layer Connection and Smoothness Strategy. *Remote Sensing*. 2016; 8(5):415.
https://doi.org/10.3390/rs8050415

**Chicago/Turabian Style**

Wang, Yongjun, Hao Xu, Liang Cheng, Manchun Li, Yajun Wang, Nan Xia, Yanming Chen, and Yong Tang.
2016. "Three-Dimensional Reconstruction of Building Roofs from Airborne LiDAR Data Based on a Layer Connection and Smoothness Strategy" *Remote Sensing* 8, no. 5: 415.
https://doi.org/10.3390/rs8050415