Point Cloud Registration Method Based on Dual Quaternion Description of Line-Planar Feature Constraints

Raobo Li; Xiping Yuan; Shu Gan; Rui Bi; Sha Gao; Yan Guo

doi:10.3788/AOS202242.0214003

Journals >Acta Optica Sinica >Volume 42 >Issue 2 >Page 0214003 > Article

Acta Optica Sinica
Vol. 42, Issue 2, 0214003 (2022)

Point Cloud Registration Method Based on Dual Quaternion Description of Line-Planar Feature Constraints

Raobo Li¹, Xiping Yuan^2、3, Shu Gan^1、2、*, Rui Bi¹, Sha Gao¹, and Yan Guo¹

Author Affiliations

¹Faculty of Land Resources and Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China

²Application Engineering Research Center of Spatial Information Surveying and Mapping Technology in Plateau and Mountainous Areas Set by Universities in Yunnan Province, Kunming, Yunnan 650093, China

³College of Geosciences and Engineering, West Yunnan University of Applied Sciences, Dali, Yunnan, 671009, China

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DOI: 10.3788/AOS202242.0214003 Cite this Article Set citation alerts

Raobo Li, Xiping Yuan, Shu Gan, Rui Bi, Sha Gao, Yan Guo. Point Cloud Registration Method Based on Dual Quaternion Description of Line-Planar Feature Constraints[J]. Acta Optica Sinica, 2022, 42(2): 0214003 Copy Citation Text

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Spatial geometric relation between straight line and plane. (a) Selected line-planar features in un-registered point cloud; (b) selected line-planar features in target point cloud

Fig. 1. Spatial geometric relation between straight line and plane. (a) Selected line-planar features in un-registered point cloud; (b) selected line-planar features in target point cloud

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Fig. 2. Flowchart of point cloud registration algorithm

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Fig. 3. Point cloud data of station 16 and station 17 before and after registration. (a) Before registration; (b) after registration

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Fig. 4. Influence of noise standard deviation on registration accuracy under different conditions. (a) Angle between lines; (b) angle between planes

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Fig. 5. Registration results of Ref. [7,14]. (a) Ref. [7]; (b) Ref. [14]

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Value	r₀	r₁	r₂	r₃	t₀	t₁	t₂	t₃	μ
Real value	0.9953	-0.0002	-0.0001	-0.0968	0.0139	-1.0697	-4.5558	0.1475	1.0000
Calculated value	0.9950	-0.0003	-0.0007	-0.0967	0.0107	-1.0690	-4.5549	0.1469	1.0002

Table 1. Real value of dual quaternion considering scale factor and calculated value of proposed method

Algorithm	Parameter	1	5	10	15	20	25
L-M	Number of iterations	68	132	503	1720	4328	8641
	Time /s	0.134	0.306	0.603	2.075	5.356	10.402
Gaussian-Newton	Number of iterations	18	-	-	-	-	-
	Time /s	0.028	-	-	-	-	-

Table 2. Number of iterations and running time of L-M algorithm and Gaussian-Newton algorithm under different initial values

Method	R	T /m	u
Theoretical value	$[\begin{array}{l} 0.9813 & 0.1927 & - 0.0001 \\ - 0.1927 & 0.9813 & 0.0003 \\ 0.0001 & - 0.0003 & 1.0000 \end{array}]$	$[\begin{array}{l} - 3.0113 \\ - 8.8617 \\ 0.2976 \end{array}]$	1.0000
Proposed method	$[\begin{array}{l} 0.9795 & 0.1934 & - 0.0012 \\ - 0.1914 & 0.9803 & 0.0015 \\ 0.0017 & 0.0005 & 1.0000 \end{array}]$	$[\begin{array}{l} - 3.0102 \\ - 8.8634 \\ 0.2954 \end{array}]$	1.0002
Ref. [7]	$[\begin{array}{l} 0.9818 & 0.1935 & - 0.0013 \\ - 0.1955 & 0.9820 & - 0.0002 \\ - 0.0024 & 0.0002 & 1.0000 \end{array}]$	$[\begin{array}{l} - 3.0120 \\ - 8.8612 \\ 0.2961 \end{array}]$	0.9999
Ref. [14]	$[\begin{array}{l} 0.9830 & 0.1928 & 0.0019 \\ - 0.1922 & 0.9814 & 0.0021 \\ - 0.0019 & 0.0018 & 1.0000 \end{array}]$	$[\begin{array}{l} - 3.0123 \\ - 8.8649 \\ 0.2952 \end{array}]$	1.0005

Table 3. Spatial transformation parameters calculated by different methods

Method	α_L /(°)	Δα_L /(°)	α_P /(°)	Δα_P /(°)	Method	α_L /(°)	Δα_L /(°)	α_P /(°)	Δα_P /(°)
Theoretical value	0.0953	0.0805	0.0934	0.0789	Proposed method	0.1619	0.1148	0.1581	0.1131
	0.0837		0.0824			0.0492		0.0501
	0.0770		0.0760			0.1081		0.1081
	0.0578		0.0570			0.0947		0.0920
	0.0230		0.0181			0.0587		0.0595
Ref. [7]	0.1469	0.1266	0.1118	0.1240	Ref. [14]	0.1374	0.1286	0.1709	0.1253
	0.0787		0.0236			0.0760		0.0114
	0.0797		0.1172			0.0718		0.0964
	0.1162		0.1274			0.1412		0.1008
	0.1283		0.1358			0.1282		0.1183

Table 4. Angle between line and line, surface and surface and their errors

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