Efficient Total Least Squares Algorithm Applied to Image Registration and Point Cloud Fitting

Zhijun Qi; wei Wang; Wenxian Zeng; Wenjie Cheng; Yelong Wei; Weiqing Zhang

doi:10.3788/CJL240581

Chinese Journal of Lasers, Volume. 51, Issue 23, 2310001(2024)

Efficient Total Least Squares Algorithm Applied to Image Registration and Point Cloud Fitting

Zhijun Qi¹, wei Wang¹, Wenxian Zeng², Wenjie Cheng¹, Yelong Wei³, and Weiqing Zhang^4、*

Author Affiliations

¹Institute of Advanced Science Facilities, Shenzhen 518107, Guangdong , China

²School of Geodesy and Geomatics, Wuhan University, Wuhan 430064, Hubei , China

³National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, Anhui , China

⁴Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, Liaoning , China

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Figures & Tables(9)

Fig. 1. STLS algorithm steps

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Fig. 2. Feature points distribution and corresponding relationships

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Fig. 3. Relationships between running time and the number of points

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Fig. 4. Registered image. (a) Wall image; (b) corresponding feature points

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Fig. 5. Distribution diagram of laser point clouds in plane. (a) Point clouds of building; (b) point clouds in plane to be fitted

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Table 1. Statistical results of parameters for different schemes

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Table 1. Statistical results of parameters for different schemes

Indicator	Scheme	${\hat{a}}_{1}$	${\hat{a}}_{2}$	${\hat{a}}_{3}$	${\hat{a}}_{4}$
E	1	0.7960	0.6965	18.5043	-2.7630
	2	0.7998	0.6999	18.5019	-2.7991
	3	0.7998	0.6999	18.5019	-2.7991
	4	0.7998	0.6999	18.5019	-2.7991
	5	0.7998	0.6999	18.5019	-2.7991
E_RMS	1	0.0045	0.0040	0.0175	0.0399
	2	0.0019	0.0020	0.0172	0.0151
	3	0.0019	0.0020	0.0172	0.0151
	4	0.0019	0.0020	0.0172	0.0151
	5	0.0019	0.0020	0.0172	0.0151

Table 2. Running time and the number of iterations for different schemes
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Table 2. Running time and the number of iterations for different schemes
Scheme $k$ $E (t)$ /s
1 1 0.0004
2 4 43.495
3 4 10.078
4 70 49.216
5 4 0.176

Table 3. Results for different schemes in the image registration
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Table 3. Results for different schemes in the image registration
Scheme ${\hat{b}}_{1}$ ${\hat{b}}_{2}$ ${\hat{b}}_{3}$ ${\hat{b}}_{4}$ $k$ $t / s$
1 0.8013 0.0985 -0.2031 1.1008 1 0.005
2 0.8006 0.0994 -0.2011 1.1005 7 35.262
3 0.8006 0.0994 -0.2011 1.1005 7 7.826
4 0.8006 0.0994 -0.2011 1.1005 84 27.943
5 0.8006 0.0994 -0.2011 1.1005 7 0.126

Table 4. Statistical results for different schemes in point cloud fitting

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Table 4. Statistical results for different schemes in point cloud fitting

Scheme	${\hat{c}}_{1}$	${\hat{c}}_{2}$	${\hat{c}}_{3}$	$σ ({\hat{c}}_{1})$	$σ ({\hat{c}}_{2})$	$σ ({\hat{c}}_{3})$	$k$	$t$ /s
1	0.24514	1.12562	$2.14 \times 10^{- 5}$	$1.22 \times 10^{- 4}$	$2.06 \times 10^{- 4}$	$3.19 \times 10^{- 4}$	1	0.001
2	0.24515	1.12559	$1.80 \times 10^{- 5}$	$0.70 \times 10^{- 4}$	$1.18 \times 10^{- 4}$	$1.83 \times 10^{- 4}$	5	49.218
3	0.24515	1.12559	$1.80 \times 10^{- 5}$	$0.70 \times 10^{- 4}$	$1.18 \times 10^{- 4}$	$1.83 \times 10^{- 4}$	5	22.317
4	0.24515	1.12559	$1.80 \times 10^{- 5}$	$0.70 \times 10^{- 4}$	$1.18 \times 10^{- 4}$	$1.83 \times 10^{- 4}$	76	42.739
5	0.24515	1.12559	$1.80 \times 10^{- 5}$	$0.70 \times 10^{- 4}$	$1.18 \times 10^{- 4}$	$1.83 \times 10^{- 4}$	5	0.381

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Zhijun Qi, wei Wang, Wenxian Zeng, Wenjie Cheng, Yelong Wei, Weiqing Zhang. Efficient Total Least Squares Algorithm Applied to Image Registration and Point Cloud Fitting[J]. Chinese Journal of Lasers, 2024, 51(23): 2310001

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