Dual-Branch 3D Surface Reconstruction Method Based on Gradient Fields

Fig. 3. Surface visualization under different noise conditions.(a) Ground truth; (b) surface with Gaussian noise; (c) surface with abnormal noise; (d) surface with mixed noise (Gaussian noise+abnormal noise)

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Fig. 4. Comparison of simulation data test results and errors of three methods (SLI, DUNet, DS-ResUNet) with initial matrix sizes of 8×8 and 2×2. (a)(e) Ground truth corresponding to initial matrix size of 8×8; (b) result of SLI; (c) result of DUNet; (d) result of DS-ResUNet; (f) error of SLI; (g) error of DUNet; (h) error of DS-ResUNet; (i)(m) ground truth corresponding to initial matrix size of 2×2; (j) result of SLI; (k) result of DUNet; (l) result of DS-ResUNet; (n) error of SLI; (o) error of DUNet; (p) error of DS-ResUNet

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Fig. 5. The facial loss change graph of each model during the network training process

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Fig. 6. Comparison of 3D surface reconstruction results and errors in practical scenarios. (a) Result of interferometer measurement; (b) result of SLI; (c) result of DUNet; (d) result of DS-ResUNet; (e) error of SLI; (f) error of DUNet; (g) error of DS-ResUNet

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Table 1. Comparison of MSE and SSIM metrics for different methods on the 32 pixel×32 pixel dataset

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Table 1. Comparison of MSE and SSIM metrics for different methods on the 32 pixel×32 pixel dataset

Noise type	MSE				SSIM
Noise type	SLI	SouthWell	DUNet	Proposed method	SLI	SouthWell	DUNet	Proposed method
No noise	0.0091	0.0198	0.0276	0.0024	0.9910	0.9576	0.9757	0.9881
Gaussian noise	0.0579	0.0667	0.0647	0.0336	0.9377	0.9412	0.9523	0.9555
Impulse noise	0.0900	0.0845	0.0145	0.0013	0.9327	0.9447	0.9684	0.9856
Mixed noise	0.5493	0.5131	0.0942	0.0375	0.8986	0.9526	0.9606	0.9670
Average	0.1766	0.1710	0.0503	0.0187	0.9400	0.9490	0.9642	0.9741

Table 2. Comparison of rRMSE and rPV metrics for different methods on the 32 pixel×32 pixel dataset

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Table 2. Comparison of rRMSE and rPV metrics for different methods on the 32 pixel×32 pixel dataset

Noise type	rRMSE /10^-15				rPV
Noise type	SLI	SouthWell	DUNet	Proposed method	SLI	SouthWell	DUNet	Proposed method
No noise	29.95	29.83	3.51	3.28	0.0220	0.0318	0.0665	0.0169
Gaussian noise	31.46	30.31	3.21	3.13	0.0961	0.0944	0.0884	0.0589
Impulse noise	30.95	31.64	3.59	3.20	0.2446	0.1993	0.0732	0.0237
Mixed noise	29.57	30.00	3.28	3.10	0.2917	0.2388	0.0775	0.0424
Average	30.48	30.53	3.40	3.18	0.1636	0.1411	0.0764	0.0355

Table 3. Comparison of MSE and SSIM metrics for different methods on the 128 pixel×128 pixel dataset

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Table 3. Comparison of MSE and SSIM metrics for different methods on the 128 pixel×128 pixel dataset

Noise type	MSE				SSIM
Noise type	SLI	SouthWell	DUNet	Proposed method	SLI	SouthWell	DUNet	Proposed method
No noise	0.00004	0.00008	0.0179	0.0031	0.9999	0.9998	0.9503	0.9880
Gaussian noise	0.0658	0.0604	0.0546	0.0338	0.8329	0.8485	0.9372	0.9552
Impulse noise	0.0096	0.0089	0.0121	0.0014	0.9626	0.9661	0.9388	0.9867
Mixed noise	0.1880	0.1731	0.1097	0.0414	0.8136	0.8301	0.9407	0.9637
Average	0.0659	0.0606	0.0486	0.0199	0.9023	0.9111	0.9418	0.9734

Table 4. Comparison of rRMSE and rPV metrics for different methods on the 128 pixel×128 pixel dataset

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Table 4. Comparison of rRMSE and rPV metrics for different methods on the 128 pixel×128 pixel dataset

Noise type	rRMSE /10^-14				rPV
Noise type	SLI	SouthWell	DUNet	Proposed method	SLI	SouthWell	DUNet	Proposed method
No noise	32.98	31.61	4.59	3.99	0.0015	0.0022	0.0660	0.0183
Gaussian noise	34.28	33.20	4.78	4.53	0.1215	0.1139	0.0803	0.0596
Impulse noise	34.11	35.51	5.15	4.38	0.0834	0.0694	0.0790	0.0215
Mixed noise	33.12	37.58	4.60	4.33	0.1943	0.1661	0.0739	0.0464
Average	33.62	34.47	4.78	4.31	0.1002	0.0879	0.0748	0.0365

Table 5. Ablation study on the 32 pixel×32 pixel dataset

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Table 5. Ablation study on the 32 pixel×32 pixel dataset

Model	Group	AFF	$L_{g r a d i e n t}$	MSE	SSIM	rRMSE /10^-15	rPV
DS-ResUNet	0			0.0279	0.9597	3.30	0.0564
	1	√		0.0241	0.9647	3.20	0.0516
	2		√	0.0197	0.9717	3.28	0.0384
	3	√	√	0.0187	0.9741	3.18	0.0355
DUNet	4			0.1268	0.9083	3.79	0.1372
DUNet	5		√	0.0503	0.9642	3.40	0.0764

Table 6. Ablation study on the 128 pixel×128 pixel dataset

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Table 6. Ablation study on the 128 pixel×128 pixel dataset

Model	Group	AFF	$L_{g r a d i e n t}$	MSE	SSIM	rRMSE /10^-14	rPV
DS-ResUNet	0			0.0854	0.9131	4.80	0.1460
	1	√		0.0313	0.9492	4.41	0.0765
	2		√	0.0729	0.9440	5.05	0.0662
	3	√	√	0.0199	0.9734	4.31	0.0365
DUNet	4			0.1605	0.8512	5.36	0.2173
DUNet	5		√	0.0486	0.9418	4.78	0.0748

Table 7. Comparison of MSE, SSIM, rRMSE, and rPV for different methods
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Table 7. Comparison of MSE, SSIM, rRMSE, and rPV for different methods
Method MSE /10^-4 SSIM rRMSE /10^-4 rPV
SLI 2.9517 0.7851 0.7592 0.4522
DUNet 5.2647 0.6950 3.0104 0.6726
DS-ResUNet 2.4665 0.8179 1.8975 0.4158

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Xuejiao Zhang, Niannian Chen, Ling Wu, Yong Fan. Dual-Branch 3D Surface Reconstruction Method Based on Gradient Fields[J]. Laser & Optoelectronics Progress, 2025, 62(16): 1612001

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Dec. 12, 2024

Accepted: Mar. 12, 2025

Published Online: Aug. 11, 2025

The Author Email: Niannian Chen (chenniannian@swust.edu.cn)

DOI:10.3788/LOP242414

CSTR:32186.14.LOP242414

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Comparison of MSE and SSIM metrics for different methods on the 32 pixel×32 pixel dataset

Table 1. Comparison of MSE and SSIM metrics for different methods on the 32 pixel×32 pixel dataset

Table 2. Comparison of rRMSE and rPV metrics for different methods on the 32 pixel×32 pixel dataset

Table 2. Comparison of rRMSE and rPV metrics for different methods on the 32 pixel×32 pixel dataset

Table 3. Comparison of MSE and SSIM metrics for different methods on the 128 pixel×128 pixel dataset

Table 3. Comparison of MSE and SSIM metrics for different methods on the 128 pixel×128 pixel dataset

Table 4. Comparison of rRMSE and rPV metrics for different methods on the 128 pixel×128 pixel dataset

Table 4. Comparison of rRMSE and rPV metrics for different methods on the 128 pixel×128 pixel dataset

Table 5. Ablation study on the 32 pixel×32 pixel dataset

Table 5. Ablation study on the 32 pixel×32 pixel dataset

Table 6. Ablation study on the 128 pixel×128 pixel dataset

Table 6. Ablation study on the 128 pixel×128 pixel dataset

Table 7. Comparison of MSE, SSIM, rRMSE, and rPV for different methods

Table 7. Comparison of MSE, SSIM, rRMSE, and rPV for different methods