# A Building Extraction Approach Based on the Fusion of LiDAR Point Cloud and Elevation Map Texture Features

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## Abstract

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## 1. Introduction

## 2. Basic Theory of Gabor Filters

## 3. Building Extraction Based on the Fusion of Point Cloud and Texture Features

#### 3.1. Point Cloud Features

#### 3.2. Texture Feature Extraction Based on the Elevation Map

#### 3.3. Feature Selection for Reducing the Number of Features

#### 3.4. Definition of the Objective Function

#### 3.5. Implementation of the Proposed Method

- Step 1: Input the testing images, and compute the feature vectors of the point cloud. Generate elevation maps, and extract texture features via the Gabor filter from them.
- Step 2: Build the training and testing samples based on the fusion of point cloud and texture features;
- Step 3: Randomly generate the initial population of PSO in the range of −10–10 via decimal coding, and transform it into binary coding;
- Step 4: Conduct building extraction, and compute the fitness value of each particle by Equation (9);
- Step 5: Operation of PSO:
- Step 6: Conduct building extraction, and compute the fitness value of each particle by Equation (9);
- Step 7: If the solution is better, replace the current particle; otherwise, the particle does not change, and then, find the current global best solution;
- Step 8: Judge whether the maximum number of iterations is reached, and if it is, go to Step 9; otherwise, go to Step 5;
- Step 9: Output the optimal feature combination, and compare it with other building extraction methods via the extraction accuracy.

## 4. Experimental Results and Discussion

#### 4.1. Experimental Platform and Data Information

#### 4.2. Extraction of Texture Features

#### 4.3. Comparative Analysis and Accuracy Evaluation of Building Extraction

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Category | Name | Abbreviation | Meaning | Formula |
---|---|---|---|---|

Eigenvalue-based features | Sum | SU | Sum of eigenvalues | ${\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3}$ |

Total variance | TV | Total variance | ${({\lambda}_{1}{\lambda}_{2}{\lambda}_{3})}^{1/3}$ | |

Eigen entropy | EI | Characteristic entropy | $-\sum _{i=-3}^{3}{\lambda}_{i}\xb7In({\lambda}_{i})$ | |

Anisotropy | AN | Anisotropy | $({\lambda}_{1}-{\lambda}_{3})/{\lambda}_{1}$ | |

Planarity | PL | Planarity | $({\lambda}_{2}-{\lambda}_{3})/{\lambda}_{1}$ | |

Linearity | LI | Linearity | $({\lambda}_{1}-{\lambda}_{2})/{\lambda}_{1}$ | |

Surface roughness | SR | Surface roughness | ${\lambda}_{3}/({\lambda}_{1}+{\lambda}_{2}+{\lambda}_{3})$ | |

Sphericity | SP | Sphericity | ${\lambda}_{3}/{\lambda}_{1}$ | |

Density-based feature | Point Density | PD | Point Density | $0.75\ast \frac{{N}_{3D}}{\pi {r}^{3}}$ |

Elevation-based features | Height above | HA | The height difference between the current point and the lowest point | $Z-{Z}_{min}$ |

Height below | HB | The height difference between the highest point and the current point | ${Z}_{max}-Z$ | |

Sphere Variance | SPV | Standard deviation of the height difference in the spherical neighborhood | $-\sqrt{\frac{\sum _{i=1}^{n}{({Z}_{i}-{Z}_{ave})}^{2}}{n-1}}$ |

**Table 2.**Experimental data information. LDR, low-density region; MDR, medium-density region; HDR, high-density region.

Experimental Data | Data Area | Number of Points | Point Cloud Density | ||
---|---|---|---|---|---|

${(\mathbf{m}}^{2})$ | Original Data | After Dilution | Original Data | After Dilution | |

LDR 1 | 174,080 | 4,486,763 | 19,320 | 25.799339 | 0.111040 |

LDR 2 | 155,595 | 3,989,310 | 21,926 | 25.683631 | 0.140958 |

MDR | 186,147 | 585,024 | 23,675 | 26.261592 | 0.183575 |

HDR 1 | 99,470 | 2,283,275 | 29,127 | 23.062170 | 0.294197 |

HDR 2 | 68,040 | 1,897,760 | 20,663 | 27.936171 | 0.303810 |

**Table 3.**Comparison of the experimental results with other methods for building extraction (%). OPCF, only point cloud features; NFS, no feature selection.

Experimental Data | GLCM | HoG | LBP | OPCF | NFS | ENVI | Proposed |
---|---|---|---|---|---|---|---|

LDR 1 | 86.9984 | 75.9503 | 88.3870 | 80.4586 | 78.7330 | 87.4203 | 90.4238 |

LDR 2 | 65.5523 | 85.1865 | 74.5297 | 85.5651 | 89.6949 | 91.3310 | 92.2558 |

MDR | 75.8902 | 78.9356 | 73.3347 | 81.7022 | 82.3527 | 83.5180 | 87.1679 |

HDR 1 | 87.5064 | 90.8264 | 90.0470 | 87.4961 | 81.6047 | 90.2660 | 92.1138 |

HDR 2 | 62.3917 | 76.6975 | 75.2795 | 79.4367 | 84.2762 | 86.2752 | 89.1207 |

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**MDPI and ACS Style**

Lai, X.; Yang, J.; Li, Y.; Wang, M.
A Building Extraction Approach Based on the Fusion of LiDAR Point Cloud and Elevation Map Texture Features. *Remote Sens.* **2019**, *11*, 1636.
https://doi.org/10.3390/rs11141636

**AMA Style**

Lai X, Yang J, Li Y, Wang M.
A Building Extraction Approach Based on the Fusion of LiDAR Point Cloud and Elevation Map Texture Features. *Remote Sensing*. 2019; 11(14):1636.
https://doi.org/10.3390/rs11141636

**Chicago/Turabian Style**

Lai, Xudong, Jingru Yang, Yongxu Li, and Mingwei Wang.
2019. "A Building Extraction Approach Based on the Fusion of LiDAR Point Cloud and Elevation Map Texture Features" *Remote Sensing* 11, no. 14: 1636.
https://doi.org/10.3390/rs11141636