Oblique Image Orientation Method Based on Local-to-Global Optimization Strategy

Fig. 1. Working principle of five camera oblique photography device. (a) Five images captured in 3D object space; (b) plane-directional distribution of five images captured on an exposure station

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Fig. 2. There is a large overlap between the images on five different exposure stations. (a) Plane-directional distribution of the five exposure stations; (b) an example of local map from ISRPS EuroSDR dataset

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Fig. 3. Principle structure of the LGO method

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Fig. 4. Combining all local maps into a global map by a least-square optimization

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Fig. 5. Spatial distribution of the exposure stations over the observed terrain

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Fig. 6. Trajectories of the nadir cameras of the exposure stations

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Fig. 7. Change of MSE with the number of iterations. (a) MSE of the BA method; (b) MSE of the LGO method

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Fig. 8. Residual of all estimated camera positions

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Fig. 9. Distribution of the 135 Zurich images and the construction of local maps

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Fig. 10. Trajectories for the Zurich data. (a) Trajectory of only nadir images; (b) Trajectory of both nadir and side images

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Fig. 11. Change of MSE with the number of iterations on the Zurich dataset. (a) BA method; (b) LGO method

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Fig. 12. Residual of 135 Zurich images estimated by the BA and LGO methods. (a) X direction; (b) Y direction; (c) Z direction; (d) 3D

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Table 1. Parameters of the large scale simulated dataset
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Table 1. Parameters of the large scale simulated dataset
Parameter Value
Area/(km×km) 60×7
Number of track points 10
Number of images 5000
Number of local maps 1000
Number of 3D points 54337
Number of projection points 490086

Table 2. RMSE of camera positions estimated by the BA and the LGO methodsunit: m
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Table 2. RMSE of camera positions estimated by the BA and the LGO methodsunit: m
Parameter BA LGO
X 9.6563 9.6516
Y 5.0619 5.0623
Z 0.8362 0.8568
3D 6.3131 6.3117

Table 3. Results of BA and LGO methods on the large scale simulated dataset with initialization noise

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Table 3. Results of BA and LGO methods on the large scale simulated dataset with initialization noise

Condition	BA method			LGO method
Condition	Initial MSE	Final MSE	Number ofiterations	Initial MSE	Final MSE	Number ofiterations
XYZ+5 m	1.922×10³	0.012	4	2.352×10³	0.004	3
XYZ+50 m	1.998×10⁵	0.012	5	2.425×10⁵	0.004	5
XYZ+100 m	7.930×10⁵	0.012	6	1.288×10⁶	0.004	6
XYZ+200 m	3.594×10⁶	Singular		5.828×10⁶	0.004	9
XYZ+300 m	2.375×10¹³	Singular		3.188×10¹³	Singular
Ang+0.1 rad	8.903×10⁵	Singular		9.805×10⁵	0.004	5
Ang+0.2 rad	3.823×10⁶	Singular		4.013×10⁶	8.343	22
Ang+0.25 rad	1.019×10⁷	Singular		6.496×10⁶	Singular
Ang+0.3 rad	2.022×10⁷	Singular		9.538×10⁶	Singular
Ang+0.4 rad	1.803×10¹²	Singular		1.677×10⁷	Singular

Table 4. Overall parameters of the used Zurich dataset

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Table 4. Overall parameters of the used Zurich dataset

Parameter	Content
Camera type	Leica RCD30 Oblique Penta
Image size /(pixel×pixel)	9000×6732
Focal length /mm	53
Pixel size /mm	0.006
Platform height /m	1000
Title angles /(°)	35
Along-track overlap /%	70
Across-track overlap /%	50
Ground sample distance(GSD) /cm	6--12
Number of images	135
Number of 3D points	51672
Number of projection points	225952

Table 5. Parameters of the BA method and the proposed method for Zurich data

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Table 5. Parameters of the BA method and the proposed method for Zurich data

Indicator	BA	LGO
Initial MSE	2.416×10⁶	1.838×10⁸
Final MSE	0.989	0.282
Number of iterations	8	4
RMSE along X-axis /m	0.1896	0.1817
RMSE along Y-axis /m	0.1704	0.1752
RMSE along Z-axis /m	0.1527	0.1535
RMSE in 3D space /m	0.1715	0.1705

Table 6. Results of BA and LGO methods on the Zurich dataset with initialization noise

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Table 6. Results of BA and LGO methods on the Zurich dataset with initialization noise

Condition	BA method			LGO method
Condition	Initial MSE	Final MSE	Number ofiterations	Initial MSE	Final MSE	Number ofiterations
XYZ+5 m	4.337×10³	0.989	5	4.383×10³	0.380	3
XYZ+50 m	4.879×10⁵	0.989	6	4.818×10⁵	0.380	3
XYZ+100 m	1.352×10⁶	0.989	8	1.288×10⁶	0.380	3
XYZ+200 m	6.971×10⁶	Singular		5.498×10⁶	0.380	3
XYZ+300 m	3.687×10¹²	Singular		1.677×10⁷	0.380	3
Ang+0.1 rad	4.119×10⁵	0.989	6	4.003×10⁵	0.380	5
Ang+0.2 rad	1.897×10⁶	0.989	7	1.675×10⁶	0.380	6
Ang+0.25 rad	3.260×10⁶	0.989	7	2.593×10⁶	0.380	7
Ang+0.3 rad	4.419×10⁶	0.989	8	3.349×10⁶	0.380	7
Ang+0.4 rad	8.364 ×10⁸	Singular		6.680×10⁶	0.380	8

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Peigen Ye, Ze Yang, Yanbiao Sun, Jigui Zhu. Oblique Image Orientation Method Based on Local-to-Global Optimization Strategy[J]. Acta Optica Sinica, 2021, 41(14): 1415001

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Paper Information

Category: Machine Vision

Received: Nov. 13, 2020

Accepted: Feb. 5, 2021

Published Online: Jul. 11, 2021

The Author Email: Sun Yanbiao (yanbiao.sun@tju.edu.cn)

DOI:10.3788/AOS202141.1415001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Parameters of the large scale simulated dataset

Table 1. Parameters of the large scale simulated dataset

Table 2. RMSE of camera positions estimated by the BA and the LGO methodsunit: m

Table 2. RMSE of camera positions estimated by the BA and the LGO methodsunit: m

Table 3. Results of BA and LGO methods on the large scale simulated dataset with initialization noise

Table 3. Results of BA and LGO methods on the large scale simulated dataset with initialization noise

Table 4. Overall parameters of the used Zurich dataset

Table 4. Overall parameters of the used Zurich dataset

Table 5. Parameters of the BA method and the proposed method for Zurich data

Table 5. Parameters of the BA method and the proposed method for Zurich data

Table 6. Results of BA and LGO methods on the Zurich dataset with initialization noise

Table 6. Results of BA and LGO methods on the Zurich dataset with initialization noise