A Hybrid Conjugate Gradient Algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair

doi:10.11947/j.JGGS.2020.0207

Journal of Geodesy and Geoinformation Science ›› 2020, Vol. 3 ›› Issue (2): 62-70.doi: 10.11947/j.JGGS.2020.0207

A Hybrid Conjugate Gradient Algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair

Jiatian LI^1,²,Congcong WANG^1,²(),Chenglin JIA^1,²,Yiru NIU^1,²,Yu WANG^1,²,Wenjing ZHANG^1,²,Huajing WU^1,²,Jian LI^1,²

1. Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China
2. Surveying and Mapping Geo-Informatics Technology Research Center, Plateau Mountains of Yunnan Higher Education of Kunming University of Science and Technology, Kunming 650093, China

Received:2019-07-25 Accepted:2020-01-25 Online:2020-06-20 Published:2020-07-08
Contact: Congcong WANG E-mail:1084719493@qq.com
About author:Jiatian LI(1975—), male, PhD, professor,majors in numerical optimization method and machine scene understanding.E-mail: ljtwcx@163.com
Supported by:
National Natural Science Foundation of China(41561082);National Natural Science Foundation of China(41161061)

Abstract

Abstract:

The fast convergence without initial value dependence is the key to solving large angle relative orientation. Therefore, a hybrid conjugate gradient algorithm is proposed in this paper. The concrete process is: ① stochastic hill climbing(SHC) algorithm is used to make a random disturbance to the given initial value of the relative orientation element, and the new value to guarantee the optimization direction is generated. ②In local optimization, a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate. ③The global convergence condition is that the calculation error is less than the prescribed limit error. The comparison experiment shows that the method proposed in this paper is independent of the initial value, and has higher accuracy and fewer iterations.

Key words: relative orientation; big rotation angle; global convergence; stochastic hill climbing; conjugate gradient algorithm

Jiatian LI,Congcong WANG,Chenglin JIA,Yiru NIU,Yu WANG,Wenjing ZHANG,Huajing WU,Jian LI. A Hybrid Conjugate Gradient Algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(2): 62-70.

Figures/Tables 8

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References 25

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Baseline vector/mm			Rotation angle/rad
B_X	B_Y	B_Z		φ	ω	κ
0.9897	-0.0865	0.1952	0.8085		-0.4833	0.6751
-0.9562	-0.0975	-0.1862	0.3906		-0.2048	-0.9036
0.9753	0.0703	-0.2459	-0.9491		-0.5013	-0.6618

Stereo pair Number	Algorithm	Baseline vector/mm			Rotation angle/rad
Stereo pair Number	Algorithm	B_X	B_Y	B_Z		φ	ω	κ
Left- right 1	Our algorithm	0.9896	-0.0864	0.1951	0.8084		-0.4833	0.6752
	Steepest descent method	0.9896	-0.0863	0.1950	0.8084		-0.4832	0.6752
	Algorithm 3	0.9895	-0.0861	0.1948	0.8083		-0.4831	0.6754
Left- right 2	Our algorithm	-0.9563	-0.0974	-0.1862	0.3906		-0.2048	-0.9036
	Steepest descent method	-0.9563	-0.0975	-0.1861	0.3906		-0.2048	-0.9036
	Algorithm 3	-0.9560	-0.0976	-0.1860	0.3907		-0.2046	-0.9037
Left- right 3	Our algorithm	0.9752	0.0703	-0.2458	-0.9491		-0.5012	-0.6617
	Steepest descent method	0.9752	0.0703	-0.2458	-0.9492		-0.5013	-0.6618
	Algorithm 3	0.9755	0.0704	-0.2461	-0.9489		-0.5012	-0.6616

Stereo pair number	Algorithm	Number of iteration
Left-right 1	Our algorithm	45
Left-right 1	Algorithm 3	56
Left-right 2	Our algorithm	40
Left-right 2	Algorithm 3	62
Left-right 3	Our algorithm	43
Left-right 3	Algorithm 3	60

Stereo pair	Algorithm	B_X/mm	B_Y/mm	B_Z/mm	φ/rad	ω/rad	κ/rad	Accuracy /μm
Image 2/ Image 1	Steepest descent method	-1.3675	-0.0162	0.0524	-1.0647	0.0698	-1.5708	2.1
	Algorithm 3	-1.3674	-0.0162	0.0521	-1.0645	0.0698	-1.5706	2.4
	Our algorithm	-1.3675	-0.0163	0.0525	-1.0648	0.0699	-1.5707	2.2
Image 3/ Image 1	Steepest descent method	-1.3911	0.0245	0.0411	-1.0297	0.0254	0.0436	1.8
	Algorithm 3	-1.3910	0.0245	0.0413	-1.0296	0.0254	0.0438	2.1
	Our algorithm	-1.3911	0.0244	0.0410	-1.0297	0.0255	0.0437	1.8

Stereo pair	Algorithm	Number of iteration
Image 2/Image 1	Our algorithm	58
Image 2/Image 1	Algorithm 3	67
Image 3/Image 1	Our algorithm	54
Image 3/Image 1	Algorithm 3	61

A Hybrid Conjugate Gradient Algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair

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