Point Cloud Registration Algorithm Based on the Model of <inline-formula><math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mi>P</mi></mrow></msub></math></inline-formula> Sparse Constraint

Bo Yang; Mingfeng Li; Ding Tan; Guangyun Zhang

doi:10.3788/LOP241845

Laser & Optoelectronics Progress, Volume. 62, Issue 12, 1215002(2025)

Point Cloud Registration Algorithm Based on the Model of $L_{1, P}$ Sparse Constraint

Bo Yang^*, Mingfeng Li, Ding Tan, and Guangyun Zhang

Author Affiliations

School of Geomatics Science and Technology, Nanjing Tech University, Nanjing 211816, Jiangsu , China

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Figures & Tables(10)

Fig. 1. Point cloud registration framework based on $L_{1, P}$ sparse constraint model

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Fig. 2. Convergence of the solution matrix varies with the number of iterations for different p values

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Fig. 3. Visualization of registration result of each algorithm on the 3DMatch dataset

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Fig. 4. Variation of feature matching recall (FMR) with distance threshold $τ_{1}$

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Fig. 5. Variation of registration recall with Gaussian noise standard deviation

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Fig. 6. Visualization of registration results of each algorithm on the KITTI dataset

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Table 1. Registration results of each algorithm on the 3DMatch dataset

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Table 1. Registration results of each algorithm on the 3DMatch dataset

Algorithm	Feature descriptor	RE /（°）	TE /cm	RMSE /cm	Algorithm	Feature descriptor	RE /（°）	TE /cm	RMSE /cm
DCP	FPFH	8.42	21.40	18.22	DCP	FCGF	8.42	21.40	18.22
3DRegNet		3.75	9.60	8.43	3DRegNet		2.74	8.13	6.15
PointNetLK		8.04	21.30	15.35	PointNetLK		8.04	21.30	15.35
SM		6.33	14.62	13.35	SM		4.34	11.32	9.63
RANSAC		5.15	13.24	10.58	RANSAC		4.88	13.63	10.23
FGR		3.94	10.13	9.59	FGR		2.87	8.42	6.41
ICP		4.03	11.84	15.72	ICP		3.50	11.43	13.69
$L_{1, P}$		2.51	7.22	5.08	$L_{1, P}$		2.09	6.74	4.84

Table 2. Registration results of each algorithm on the KITTI dataset
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Table 2. Registration results of each algorithm on the KITTI dataset
Algorithm Feature descriptor RE /（°） TE /cm RMSE /m
RANSAC FPFH 0.93 19.66 0.31
FGR 0.86 43.84 1.6317
$L_{1, P}$ 0.71 10.58 0.192
RANSAC FCGF 0.48 18.00 0.22
FGR 0.36 25.72 0.27
$L_{1, P}$ 0.45 8.08 0.15

Table 3. Registration result of traditional registration methods combined with $L_{1, P}$

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Table 3. Registration result of traditional registration methods combined with $L_{1, P}$

Algorithm	Feature descriptor	RE /（°）	TE /cm	RMSE /m
RANSAC	FPFH	2.4328	69.3594	1.1298
FGR		1.1975	233.6941	2.4020
SM		105.4721	845.5836	38.3274
RANSAC+ $L_{1, P}$		1.2297	49.3082	0.6453
FGR+ $L_{1, P}$		1.5043	45.5449	0.7264
SM+ $L_{1, P}$		1.5051	46.6394	0.7436
RANSAC	FCGF	1.2624	94.4119	1.0447
FGR		0.3550	43.9314	0.4270
SM		0.6501	15.2060	0.2980
RANSAC+ $L_{1, P}$		0.4307	9.1393	0.1417
FGR+ $L_{1, P}$		0.3947	8.4352	0.1847
SM+ $L_{1, P}$		0.3561	7.2926	0.1654

Table 4. Ablation experimental results on 3DMatch dataset

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Table 4. Ablation experimental results on 3DMatch dataset

Feature descriptor	SM	$L_{1, P}$	MC	RMSE /cm	RE /（°）	TE /cm
FPFH	√			13.348	6.326	14.620
		√		23.560	19.623	22.808
	√		√	12.902	6.248	13.707
	√	√		12.753	6.132	12.059
		√	√	21.610	17.816	20.998
	√	√	√	5.080	2.510	7.220
FCGF	√			9.625	4.336	11.321
		√		28.119	9.091	16.067
	√		√	8.308	3.700	10.419
	√	√		8.132	3.520	9.087
		√	√	16.731	7.907	16.935
	√	√	√	4.840	2.090	6.740

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Bo Yang, Mingfeng Li, Ding Tan, Guangyun Zhang. Point Cloud Registration Algorithm Based on the Model of $L_{1, P}$ Sparse Constraint[J]. Laser & Optoelectronics Progress, 2025, 62(12): 1215002

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