# Studies on Three-Dimensional (3D) Modeling of UAV Oblique Imagery with the Aid of Loop-Shooting

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## Abstract

**:**

## 1. Introduction

^{2}area of the campus, loop-shooting-aided technology was used to achieve the goal of building a refined 3D large-scene model. This approach can provide a useful reference and scientific guidance for fields such as stereo measurement, archaeological excavations, and smart cities.

## 2. Study Area and Data

#### 2.1. Experimental Equipment

_{1}, K

_{2}, K

_{3}, P

_{1}and P

_{2}. Consequently, the UAV cameras were calibrated, and the obtained camera-related parameters are listed in Table 2.

#### 2.2. Description of the Experimental Data

#### 2.2.1. Selection of the Research Area

^{2}, and its average elevation is above 1900 m. The airflow was relatively stable during the photographing process, and the pressure was moderate, which is conducive to acquiring high-quality aerial images. Moreover, the research area has good transportation and an open space far away from the airport and other no-fly zones, which were convenient for UAS equipment transportation, takeoff and landing. In addition, the research area includes rich geospatial features. For example, it includes buildings with various geometrical characteristics and heights, water bodies, vegetation, and roads, which have a universal representation. The research area is shown in Figure 2.

#### 2.2.2. Acquisition of Experimental Data

## 3. Methods

#### 3.1. The 3D Modeling Process

#### 3.1.1. Data Preprocessing

#### 3.1.2. POS-Aided Aerotriangulation

#### 3.1.3. Construction of the 3D Model

#### 3.2. Incremental 3D Modeling with the Aid of Loop-Shooting

#### 3.2.1. Incremental Modeling with the Aid of Loop-Shooting

_{j}is the j

_{th}defective region s.

_{th}loop-shooting image set is denoted as RI

_{n}. A schematic flow chart of the loop-shooting process is shown in Figure 5. While acquiring images, the overlap rate must be ensured in every two adjacent images (such as a 75% overlap rate). In addition, the acquisition process must ensure that a sufficient number of matching points will exist between the loop-shooting images and the original UAV images. The specific strategies adopted are as follows: select an image in advance to calculate the corresponding matching points using a threshold of 70% of the total image matching points. Then, determine the matching points of the other loop-shooting images. Image whose matching points exceed the threshold are retained; the others are deleted.

_{0}, y

_{0}) represents the coordinate of the principal point of the image; (X, Y, Z) represents the ground point corresponding to the image point coordinate; (X

_{S}, Y

_{S}, Z

_{S}) represents the projection center coordinate; and $\left[\begin{array}{ccc}{a}_{1}& {b}_{1}& {c}_{1}\\ {a}_{2}& {b}_{2}& {c}_{2}\\ {a}_{3}& {b}_{3}& {c}_{3}\end{array}\right]$ represents the matrix of the rotation transformation.

_{i}can be calculated by the ground control point and the corresponding image point. There are 11 coefficients in Equation (3); therefore, solving it requires a minimum of 6 control points.

_{n}is the aerotriangulation result after the n

_{th}incremental iterative calculation, $R{I}_{n}$ is the image set from the n

_{th}loop-shooting, and x

_{0}is the initial results of the aerotriangulation.

#### 3.2.2. Precision Verification and Model Refinement

## 4. Experimental Results

#### 4.1. POS-Aided Aerotriangulation Results

#### 4.2. Initial 3D Modeling Results

#### 4.3. Incremental Modeling with the Aid of Loop-Shooting

#### 4.4. Refined 3D Modeling

## 5. Discussion

_{rj}, Dis, 3D, x, and y, respectively, and denote the differences in the indexes before and after loop-shooting by ∆P

_{rj}, ∆Dis, ∆3D, ∆x, and ∆y, respectively. The results of the comparisons of these different indexes are shown in Table 3.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) is a multirotor unmanned aerial vehicle; (

**b**) is a five-lens camera carried by the UAV.

**Figure 7.**(

**a**) The 3D triangulation results for part of the region; (

**b**) Zoomed-in 3D triangulation results.

**Figure 8.**(

**a**) Original digital surface model (DSM); (

**b**) Initial 3D model after performing texture mapping.

**Figure 9.**(

**a**–

**d**) Representations of the aerotriangulation results aided by varying levels of loop-shooting.

**Figure 10.**The 3D model results for the “Fontaine Blanche Hotel:” (

**a**) the overall and regional 3D results for the original model; (

**b**) the overall and regional 3D results aided by one loop-shooting operation; (

**c**) the overall and regional 3D results aided by a second loop-shooting operation; and (

**d**) the overall and regional 3D results aided by a third loop-shooting operation.”.

**Figure 11.**Final results: (

**a**) the refined model for the entire research region; (

**b**) the refined model for the side of the “Fontaine Blanche Hotel”; (

**c**) the refined model for the front of the “Fontaine Blanche Hotel”.

Flight Platform | UAV Configuration |
---|---|

Focal length | 16 mm |

Image pixels | 4000 × 6000 |

Main point (x, y) | (2999.5, 1999.5) |

Pixel size | 4 μm |

Camera sensor | CCD |

Number of shots | 4 tilted lenses, 1 vertical lens |

Lens tilt angle | 45° |

Camera | Parameters Symbol | Value |
---|---|---|

Focal length (mm) | F | 16 |

Radial distortion (mm) | K_{1} | −2.93279097580502 × 10^{−10} |

Radial distortion (mm) | K_{2} | 2.71144019108787 × 10^{−17} |

Radial distortion (mm) | K_{3} | −7.632447492096 × 10^{−26} |

Tangential distortion (mm) | P_{1} | −1.0747635629201 × 10^{−10} |

Tangential distortion (mm) | P_{2} | −5.08835248657514 × 10^{−11} |

**Table 3.**Results of the comparison of different indexes of the 3D triangulation before and after compensation loop-shooting.

Type | P_{rj} (px) | Dis (m) | 3D (m) | X (m) | Y (m) | ∆P_{rj} (px) | ∆Dis (m) | ∆3D (m) | ∆x (m) | ∆y (m) | |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | Original | 0.1 | 0.002 | 0.004 | 0.002 | −0.004 | −0.16 | −0.001 | −0.002 | 0 | −0.001 |

1 | Loop-shooting | 0.26 | 0.003 | 0.006 | 0.002 | −0.005 | |||||

2 | Original | 0.5 | 0.014 | 0.017 | 0.014 | 0.01 | 0.05 | 0.005 | 0.003 | 0.005 | 0 |

2 | Loop-shooting | 0.45 | 0.009 | 0.014 | 0.009 | 0.01 | |||||

3 | Original | 0.88 | 0.021 | 0.021 | 0.005 | −0.021 | 0.08 | 0.01 | 0.009 | −0.004 | 0.013 |

3 | Loop-shooting | 0.8 | 0.011 | 0.012 | 0.009 | −0.008 | |||||

4 | Original | 0.67 | 0.012 | 0.016 | 0.003 | 0.016 | 0.2 | 0.004 | 0.006 | −0.006 | 0.012 |

4 | Loop-shooting | 0.47 | 0.008 | 0.01 | 0.009 | 0.004 | |||||

5 | Original | 0.07 | 0.002 | 0.002 | 0.002 | 0 | −0.34 | −0.003 | −0.005 | 0.001 | 0.005 |

5 | Loop-shooting | 0.41 | 0.005 | 0.007 | 0.001 | −0.007 | |||||

6 | Original | 0.27 | 0.007 | 0.008 | 0.007 | 0.002 | −0.49 | 0.001 | 0.002 | 0.003 | −0.003 |

6 | Loop-shooting | 0.76 | 0.006 | 0.006 | 0.004 | 0.005 | |||||

7 | Original | 0.49 | 0.012 | 0.013 | 0.011 | −0.006 | 0.22 | 0.008 | 0.007 | 0.006 | 0.003 |

7 | Loop-shooting | 0.27 | 0.004 | 0.006 | 0.005 | −0.003 |

Number | ALL_P | Med_P | All_P_{rj} (px) | All_Dis (m) |
---|---|---|---|---|

1 | 24,477 | 1,069 | 0.71 | 0.018 |

2 | 67,442 | 1,060 | 0.69 | 0.019 |

3 | 86,204 | 1,170 | 0.68 | 0.017 |

4 | 161,145 | 1,371 | 0.69 | 0.016 |

10 (m) | 20 (m) | 30 (m) | 40 (m) | 50 (m) | 100 (m) | 200 (m) | |
---|---|---|---|---|---|---|---|

Observation distance (m) after mending (m) | 10.02 | 20.3 | 30.09 | 40.04 | 50.03 | 100.07 | 200.12 |

Error value (m) | 0.02 | 0.03 | 0.09 | 0.04 | 0.03 | 0.07 | 0.12 |

Relative accuracy (%) | 99.80 | 99.85 | 99.70 | 99.90 | 99.94 | 99.93 | 99.94 |

**Table 6.**Error and relative accuracy of detailed observations before and after the loop-shooting-aided model reconstruction.

Small Window | Front Door | Footstep | Back Door | French Window | Stone Pillar | Side Door | |
---|---|---|---|---|---|---|---|

Field observation distance (m) | 2.75 | 15.38 | 15.93 | 4.23 | 6.39 | 1.32 | 6.41 |

Observation distance before mending (m) | 2.65 | 15.22 | 15.86 | 4.11 | 6.14 | 1.22 | 6.52 |

Observation distance after mending (m) | 2.73 | 15.34 | 15.91 | 4.20 | 6.26 | 1.30 | 6.37 |

Error value before mending (m) | 0.10 | 0.16 | 0.07 | 0.12 | 0.25 | 0.10 | 0.11 |

Error value after mending (m) | 0.02 | 0.04 | 0.02 | 0.03 | 0.13 | 0.02 | 0.04 |

Relative accuracy (%) | 99.27 | 99.74 | 99.87 | 99.29 | 97.97 | 98.48 | 99.38 |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; Yao, Y.; Duan, P.; Chen, Y.; Li, S.; Zhang, C.
Studies on Three-Dimensional (3D) Modeling of UAV Oblique Imagery with the Aid of Loop-Shooting. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 356.
https://doi.org/10.3390/ijgi7090356

**AMA Style**

Li J, Yao Y, Duan P, Chen Y, Li S, Zhang C.
Studies on Three-Dimensional (3D) Modeling of UAV Oblique Imagery with the Aid of Loop-Shooting. *ISPRS International Journal of Geo-Information*. 2018; 7(9):356.
https://doi.org/10.3390/ijgi7090356

**Chicago/Turabian Style**

Li, Jia, Yongxiang Yao, Ping Duan, Yun Chen, Shuang Li, and Chi Zhang.
2018. "Studies on Three-Dimensional (3D) Modeling of UAV Oblique Imagery with the Aid of Loop-Shooting" *ISPRS International Journal of Geo-Information* 7, no. 9: 356.
https://doi.org/10.3390/ijgi7090356