# Building Point Detection from Vehicle-Borne LiDAR Data Based on Voxel Group and Horizontal Hollow Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Voxel Group-Based Shape Recognition

#### 2.1.1. Voxelization

#### 2.1.2. Generating of Voxel Group

**Building 3D voxel grid system**. Set an appropriate size S to build a regular 3-D voxel grid system. Each LiDAR point is added to each voxel according to its 3D coordinates. The minimum value among all LiDAR point coordinates $({x}_{\mathrm{min}},{y}_{\mathrm{min}},{z}_{\mathrm{min}})$ is the origin of the 3D voxel grid system. For each LiDAR point, the row, column, and layer number $(i,j,k)$ of its corresponding voxel are recorded to construct a two-way index.

**Dividing voxels in each column (in vertical direction)**. On account of a series of voxels distributed in the same vertical direction, the group of voxels with the same row and column $(i,j)$ may belong to a different target, such as pedestrians or vehicles below the canopy of trees along a street. Therefore, these voxels must be separated to ensure that each voxel group contains only one object’s points, as shown in Figure 2c. Accordingly, the elevation difference between voxel ${V}_{(i,j,k)}$ and the voxel above it, ${V}_{(i,j,k+1)}$ should be calculated:

**Merging process in horizontal direction for voxel group**. A full λ-Schedule algorithm is to be taken to merge the voxel columns in horizontal direction. The full λ-Schedule algorithm [55] was first used to segment SAR images. The segmentation principle is based on the Mumford–Shah energy equation to judge the difference in object attributes and the complexity of the object boundary [11]. The merging cost value ${t}_{i,j}$ of each adjacent voxel column $({S}_{i}^{},{S}_{j})$ is calculated as below:

- Take a simple region growth for whole voxel columns in horizontal direction based on connectivity to get several rough clusters: $\{{C}_{1},{C}_{2},\dots ,{C}_{n},\dots \}$.
- Compute all the pairs of adjacent voxel columns within C
_{n}and their merging cost value from Equation (6) and sort them into a list. - Merge the pair (S
_{i},S_{j}) which own smallest t_{i,j}to form a new voxel column S_{ij}and update the merging cost value. - Repeat the step ii and step iii until the t
_{i,j}exceeds the threshold T_{End}or all the voxel columns within C_{n}into one group. - Repeat the step ii, iii, iv until all clusters are processed.

_{2}(mn))for a 2D image of m × n pixels [56]. For 3D voxel grid system, the computational complexity will be higher so the origin 3D voxel grid system must be divided into pieces to reduce the amount of involved voxel columns in one process. Finally, all voxel columns are combined into a higher-level structure, the voxel group. The LiDAR points within each voxel group belong to the same single real-world object and have the same geometric properties or shape information.

#### 2.1.3. Shape Recognition of Each Voxel Group

**Finding the center voxel**. The point density of each voxel within one voxel group is calculated and finds the most dense voxel ${V}_{md}$. Calculate the center coordinate of points in this voxel:

**Determine the variation range of neighborhood size**. Centering on $\left(\overline{X},\overline{Y},\overline{Z}\right)$, the minimum neighborhood size ${R}_{\mathrm{min}}$ is determined as the radius that includes the minimal number ${N}_{p}$ of points required for PCA. Set the increment ${R}_{i}$, the neighborhood size will increase until the radius reach the boundary of voxel group. Then the variation range of neighborhood size $\left[{R}_{\mathrm{min}},{R}_{\mathrm{max}}\right]$ is obtained.

**Calculate the dimensionality features and entropy feature**. Then the dimensionality features ${a}_{1d}^{}$, ${a}_{2d}^{}$, ${a}_{3d}^{}$ and entropy feature ${E}_{f}({V}_{p}{}^{r})$ within ${V}_{p}^{R}$ ($R\in \left[{R}_{\mathrm{min}},{R}_{\mathrm{max}}\right]$) are calculated by the Equation (9). In this paper, P denotes the center coordinate of points in the selected voxel. Then the optimal neighborhood size can be obtained:

#### 2.2. Category-Oriented Merging

#### 2.2.1. Removing Ground Points

**Extracting the potential voxel group that contains ground points**. The difference value between the lowest and highest points is calculated for each planar voxel group with an angle between the surface normal vector and horizontal plane that is greater than 85°:

**Combining the connected region**. If the elevation difference between two adjacent candidate voxel groups contains ground points less than 0.3 m, then the two voxel groups are merged. Repeat this process and calculate the area of the final combined voxel group:

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**Removing ground points**. Set the area threshold 10 m

^{2}to filter the too small combined voxel group. Then all candidate voxel groups’ average elevation are recorded and the outliers are rejected, always indicating the suspended flat roof. All the points within the rest of candidate voxel groups will be labeled as ground points and need to be removed before the next step.

#### 2.2.2. Category-Oriented Merging

#### 2.3. Horizontal Hollow Ratio-Based Building Point Identification

**Extracting outline**. The proposed method makes every segment’s voxels project to the horizontal plane to form two-dimensionality grids and employ the simple and efficient method proposed by Yang [1] to extract the contour grid: if eight neighbor grids of one background grid (contains no points) are not all background grid, it will be labeled as contour grid. The aim of this step is to reduce the amount of calculation in next step.

**Generating convex hull**. When get the contour grids of one segment, the convex hull of this segment is calculated by the Graham’s Scan method. Furthermore, the convex hull area ${S}_{C}$ of this segment can be calculated.

**Calculating horizontal hollow ratio**. The proposed method defines the horizontal hollow ratio of each voxel cluster to indicate the above feature:

**Calculating threshold**. OTSU is an automatic and unsupervised threshold selection method. Based on this method, the optimal threshold selection should be made with the best separation of the two types obtained by the threshold segmentation. The interclass separability criterion is the best statistical difference between class characteristics of maximum or minimum differences within class characteristics [59]. The building’s hollow ratio is far smaller than that of other objects, as indicated by Figure 7; therefore, using the OTSU method to obtain threshold T of the hollow ratio of the divided building and other objects should achieve a good effect:

## 3. Results and Discussion

#### 3.1. Study Area and Experimental Data

^{2}. Due to the amount of testing data being huge, the proposed method is unable to process it in one time. Therefore, we clip the raw testing data into 12 parts according to the road segments in practice. The experimental region contained both downtown area and urban residential area with a number of commercial and residential architecture. A shopping mall, a skyscraper, an apartment building, and a high-rise office building are the main architecture buildings in the study area. Due to the good road greening, a large number of street trees exist in the study area, which cause strong variation of point densities of building façade. On the other hand, it is sometimes difficult separate the buildings and the trees surround it.

#### 3.2. Extraction Results of Building Points

#### 3.3. Evaluation of Extraction Accuracy

#### 3.3.1. Building-Based Evaluation for Overall Experimental Area

#### 3.3.2. Point-Based Evaluation for Individual Building

#### 3.4. Experiment Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

LD | linear dichroism |

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**Figure 2.**Construction of voxel group. (

**a**) Point clouds distribution of several objects in a 3D voxel grid system; (

**b**) Street lamp point clouds and the generated voxels; This is a typical case in which the voxels with the same horizontal and vertical coordinates with adjacent elevations belong to the same target; (

**c**) Schematic of the process of dividing the voxel distributions on the same vertical direction; (

**d**) Profile of part canopy of a street tree, a case that adjacent voxel within points belong to one object have little elevation differences.

**Figure 5.**Voxel group-based shape recognition. (

**a**) Raw LiDAR point clouds include building facades, street trees, street lamps, cars, and the ground; (

**b**) Generated voxel group, voxels of the same color belong to the same voxel group; (

**c**) LiDAR points within each voxel group, points of the same color belong to the same voxel group; (

**d**) Shape recognition results.

**Figure 6.**Category-oriented merging. (

**a**) Merging results, points of the same color belong to the same segment; (

**b**–

**e**) I: Single real-world object with several voxel groups, points of the same color belong to the same voxel group; II: Shapes of one object, red denotes linear points, green denotes surface points, and blue denotes spherical points.

**Figure 7.**Horizontal hollow ratio-based building point identification (

**a**–

**c**).

**Left**: top view of segments of point clouds of several buildings, trees and cars.

**Right**: overlay of a convex hull and point clouds of each segment.

**Figure 9.**Experimental area. (

**a**) Aerial orthophotos of the experimental area, red line denotes the SSW mobile mapping system’s driving route; (

**b**) Raw VLS data of the experimental area.

**Figure 10.**Building point extraction results. (

**a**) Extraction results of buildings in the experiment region; (

**b**,

**c**) Proposed method successfully detected various building shapes, including skyscrapers and low cottages; (

**d**) Proposed method effectively separated a building and the trees attached to it; (

**e**) Results show that the method could also recognize buildings with sparse LiDAR points or lack of partial structures.

**Figure 11.**Point-based evaluation for individual building. (

**a**) Automatic extraction results of a building; (

**b**) Manual extraction results of the same building; (

**c**) Overlay result with the correct, error, and missing points denoted in blue, red, and yellow, respectively.

**Figure 12.**Comparison of building extraction result between the proposed method and the method of Yang et al. [37]. (

**a**–

**e**) Left to right: street image, raw VLS data, the result by the proposed method and the result by Yang’s method of the specific building.

Linear | Planar | Spherical | |
---|---|---|---|

Linear | If: $\mathrm{arccos}\theta <\overrightarrow{{p}_{s}},\overrightarrow{{p}_{c}}>\le {10}^{\circ}$&& $\left|e{t}_{s}-e{t}_{p}\right|\le {T}_{e}$ && $\Vert {o}_{s}(x,y,z)-{o}_{p}(x,y,z)\Vert <{T}_{o}$ Else if: $\mathrm{arccos}\theta <\overrightarrow{{p}_{s}},\overrightarrow{{p}_{c}}>\ge {80}^{\circ}$&& ${S}_{M\text{in}}\le {T}_{md}$ | If: $\mathrm{arccos}\theta <\overrightarrow{{p}_{s}},\overrightarrow{{n}_{c}}>\le {10}^{\circ}$|| $\mathrm{arccos}\theta <\overrightarrow{{p}_{s}},\overrightarrow{{n}_{c}}>\ge {80}^{\circ}$ && ${S}_{M\text{in}}\le {T}_{md}$ | If: $\Vert {o}_{s}(x,y)-{o}_{p}(x,y)\Vert <{T}_{o}$&& ${S}_{M\text{in}}\le {T}_{md}$ |

Planar | If: $\mathrm{arccos}\theta <\overrightarrow{{n}_{s}},\overrightarrow{{p}_{c}}>\le {10}^{\circ}$|| $\mathrm{arccos}\theta <\overrightarrow{{n}_{s}},\overrightarrow{{p}_{c}}>\ge {80}^{\circ}$ && ${S}_{M\text{in}}\le {T}_{md}$ | If: $\mathrm{arccos}\theta <\overrightarrow{{n}_{s}},\overrightarrow{{n}_{c}}>\le {10}^{\circ}$&& $\left|e{t}_{s}-e{t}_{p}\right|\le {T}_{e}$ Else if: $\mathrm{arccos}\theta <\overrightarrow{{n}_{s}},\overrightarrow{{n}_{c}}>\ge {80}^{\circ}$&& ${S}_{M\text{in}}\le {T}_{md}$ | |

Spherical | If: $\Vert {o}_{s}(x,y)-{o}_{p}(x,y)\Vert <{T}_{o}$ | If: $\Vert {o}_{s}(x,y,z)-{o}_{p}(x,y,z)\Vert <{T}_{o}$ |

Items | Values | Description | Setting Basis | |
---|---|---|---|---|

Voxel group generating | $S$ | 0.5 m | The voxel size | Empirical |

${T}_{S}$ | 0.2 m | To divide the adjacent voxel in vertical direction | Data source | |

${T}_{End}$ | 0.85 | To terminate the growth of voxel groups’ generating | Chen et al. [11] | |

Shape recognition | ${N}_{p}$ | 5 pts | Minimum number of points for PCA | Empirical |

${R}_{i}$ | 0.1 m | The increment of the search radius | Empirical | |

Category-oriented merging | ${T}_{e}$ | 0.1 m | Maximal difference of elevation between two voxel groups | Data source |

${T}_{o}$ | 0.5 m | Maximal distance between two voxel groups’ center | Empirical | |

${T}_{md}$ | 0.15 m | Maximal minimum euclidean distance between two voxel groups | Data source | |

Building point identification | $T$ | Automatic | The threshold of the horizontal hollow ratio to identify building points | Calculation |

$\overline{H}$ | 2.5 m | Minimum average height of voxel cluster | Data source | |

$Csa$ | 3 m^{2} | Minimum Cross-sectional area of voxel cluster | Data source |

Type | Number of Points | Completeness (%) | Correctness (%) | Average Com (%) | Average Corr (%) | ||
---|---|---|---|---|---|---|---|

TP | FN | FP | |||||

Low-rise | 15,744 | 500 | 1239 | 96.9 | 92.7 | 94.8 | 93.1 |

54,399 | 2233 | 349 | 96.1 | 99.4 | |||

6750 | 0 | 598 | 100 | 91.9 | |||

6830 | 377 | 135 | 94.8 | 98.1 | |||

30,752 | 3234 | 3827 | 90.5 | 88.9 | |||

38,580 | 0 | 5122 | 100 | 88.3 | |||

20,751 | 1705 | 512 | 92.4 | 97.6 | |||

8048 | 0 | 1147 | 100 | 87.5 | |||

23,606 | 3234 | 336 | 87.7 | 98.6 | |||

12,083 | 1473 | 1639 | 89.1 | 88.1 | |||

Medium-rise | 167,478 | 934 | 2126 | 99.4 | 98.7 | 95.0 | 95.7 |

85,670 | 543 | 1408 | 99.4 | 98.4 | |||

194,255 | 1560 | 3210 | 99.2 | 98.4 | |||

198,123 | 846 | 1042 | 99.6 | 99.5 | |||

125,507 | 6835 | 773 | 94.8 | 99.4 | |||

237,798 | 11,732 | 10,592 | 95.3 | 95.7 | |||

50,687 | 10,466 | 5872 | 82.9 | 89.6 | |||

219,639 | 9897 | 5396 | 95.7 | 97.6 | |||

45,340 | 3699 | 1146 | 92.5 | 97.5 | |||

25,536 | 2229 | 5587 | 92.0 | 82.0 | |||

High-rise | 115,343 | 14,306 | 388 | 89.0 | 99.7 | 91.0 | 99.4 |

186,558 | 6697 | 2993 | 96.5 | 98.4 | |||

253,489 | 14,368 | 1152 | 94.6 | 99.5 | |||

206,176 | 6467 | 1388 | 97.0 | 99.3 | |||

209,904 | 38,477 | 3387 | 84.5 | 98.4 | |||

320,217 | 26,779 | 432 | 92.3 | 99.9 | |||

153,428 | 26,186 | 0 | 85.4 | 100.0 | |||

144,498 | 10,957 | 0 | 93.0 | 100.0 | |||

54,596 | 9874 | 0 | 84.7 | 100.0 | |||

133,353 | 9248 | 652 | 93.5 | 99.5 | |||

Complex | 313,922 | 22,428 | 1716 | 93.3 | 99.5 | 91.9 | 99.0 |

34,455 | 1798 | 254 | 95.0 | 99.3 | |||

26,540 | 739 | 613 | 97.3 | 97.7 | |||

11,945 | 4250 | 0 | 73.8 | 100.0 | |||

17,711 | 2415 | 136 | 88.0 | 99.2 | |||

608,188 | 24,904 | 0 | 96.1 | 100.0 | |||

281,385 | 26,653 | 342 | 91.3 | 99.9 | |||

282,115 | 11,010 | 2341 | 96.2 | 99.2 | |||

19,957 | 832 | 687 | 96.0 | 96.7 | |||

312,765 | 27,144 | 4336 | 92.0 | 98.6 |

Point Organization | Shape Recognition | Merging | Total | |
---|---|---|---|---|

The proposed method(s) | 4.32 | 9.91 | 9.45 | 23.68 |

Yang’s method(s) | 7.67 | 10.44 | 16.96 | 35.07 |

© 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.; Cheng, L.; Chen, Y.; Wu, Y.; Li, M.
Building Point Detection from Vehicle-Borne LiDAR Data Based on Voxel Group and Horizontal Hollow Analysis. *Remote Sens.* **2016**, *8*, 419.
https://doi.org/10.3390/rs8050419

**AMA Style**

Wang Y, Cheng L, Chen Y, Wu Y, Li M.
Building Point Detection from Vehicle-Borne LiDAR Data Based on Voxel Group and Horizontal Hollow Analysis. *Remote Sensing*. 2016; 8(5):419.
https://doi.org/10.3390/rs8050419

**Chicago/Turabian Style**

Wang, Yu, Liang Cheng, Yanming Chen, Yang Wu, and Manchun Li.
2016. "Building Point Detection from Vehicle-Borne LiDAR Data Based on Voxel Group and Horizontal Hollow Analysis" *Remote Sensing* 8, no. 5: 419.
https://doi.org/10.3390/rs8050419