Deep learning spatial phase unwrapping: a comparative review

Kaiqiang Wang; Qian Kemao; Jianglei Di; Jianlin Zhao

doi:10.1117/1.APN.1.1.014001

Advanced Photonics Nexus, Volume. 1, Issue 1, 014001(2022)

Deep learning spatial phase unwrapping: a comparative review Article Video

Kaiqiang Wang1...2, Qian Kemao3,*, Jianglei Di1,2,4,*, and Jianlin Zhao12,* |Show fewer author(s)

¹Northwestern Polytechnical University, School of Physical Science and Technology, Shaanxi Key Laboratory of Optical Information Technology, Xi’an, China

²Ministry of Industry and Information Technology, Key Laboratory of Light Field Manipulation and Information Acquisition, Xi’an, China

³Nanyang Technological University, School of Computer Science and Engineering, Singapore

⁴Guangdong University of Technology, Guangdong Provincial Key Laboratory of Photonics Information Technology, Guangzhou, China

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Figures & Tables(32)

Fig. 1. Phase unwrapping in OI,¹ MRI,² FPP,⁴ and InSAR.⁶

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Fig. 2. Datasets of the deep-learning-involved phase unwrapping methods, for (a) dRG, (b) dWC, and (c) dDN. “ $R$ ” and “ $I$ ” represent the real and imaginary parts of CAF, respectively.

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Fig. 3. Overall process of deep-learning-involved phase unwrapping methods.

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Fig. 4. Illustration of the dRG method.

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Fig. 5. Illustration of the dWC method.

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Fig. 6. Illustration of the dDN method.

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Fig. 7. An example of the RME method.

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Fig. 8. An example of the GFS method.

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Fig. 9. Entropy histogram of absolute phases from the D_RME, D_GFS, and D_ZPS.

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Fig. 10. SAGD maps of different datasets. Red arrows and circles indicate low and high SAGD values, respectively.

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Fig. 11. Mean error maps for each network. Red circles indicate high mean error value.

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Fig. 12. (a) SAGD maps for D_RME and D_RME1, (b) mean error maps for RME-Net and RME1-Net. Red arrows indicate low SAGD value. Red circles indicate high mean error value and orange circles indicate the comparison part.

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Fig. 13. Partial display of results from RME1-Net. “Max”, “Med,” and “Min” represent specific results with maximal, median, and minimal ${RMSE}_{m}$ , respectively. “-C” represents the congruence results.

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Fig. 14. Results for the (a) dRG-I and (b) dWC-I in the ideal case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal ${RMSE}_{m}$ , respectively. “-C” represents the congruence results.

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Fig. 15. ${RMSE}_{m}$ of the deep-learning-involved methods for absolute phase in different heights.

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Fig. 16. Results for (a) dRG-N, (b) dWC-N, and (c) dDN-N in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal ${RMSE}_{m}$ , respectively. “-C” represents the congruence results.

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Fig. 17. Results in different noise levels. Solid and dashed lines represent the deep-learning-involved and traditional methods, respectively.

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Fig. 18. Results for (a) dRG-I, (b) dWC-I, (c) dRG-D, (d) dWC-D, (e) line-scanning, (f) LS, and (g) QG methods in the discontinuous case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal ${RMSE}_{m}$ , respectively. “-C” represents the congruence results. The last columns of each result are discontinuous maps, where 1 (white) represents the position of the discontinuous pixels.

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Fig. 19. Results for (a) dRG-A, (b) dWC-A, (c) line-scanning, (d) LS, and (e) QG methods in the aliasing case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal ${RMSE}_{m}$ , respectively. “-C” represents the congruence results. The last columns of each result are aliasing maps, where 1 (white) represents the position of the aliasing pixels.

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Fig. 20. Results for (a) dRG-M, (b) dWC-M, (c) line-scanning, (d) LS, and (e) QG methods in the mixed case. “Max,” “Med,” and “Min” represent specific results with maximal, median, and minimal ${RMSE}_{m}$ , respectively. “ $- C$ ” represents the congruence results. The last columns of each result are aliasing or discontinuous maps (called “ $A$ and $D$ ”), where 1 (white) represents the position of the aliasing or discontinuous pixels.

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Fig. 21. Schematic diagram of pretraining and retraining.

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Fig. 22. Loss plot of pretrained and initialized networks.

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Table 1. Summary of deep-learning-involved phase unwrapping methods. “—” indicates “not available.”

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Table 1. Summary of deep-learning-involved phase unwrapping methods. “—” indicates “not available.”


Method	Date	Author	Ref.	Network	Dataset	Loss function
dRG	2018	Dardikman and Shaked	22	—	—	—
Dardikman et al.	23	ResNet	RDR	MSE
2019	Wang et al.	24	Res-UNet	RME	MSE
He et al.	25	3D-ResNet	—	—
Ryu et al.	26	RNN	—	Total variation + error variation
2020	Dardikman-Yoffe et al.	27	Res-UNet	RDR	MSE
Qin et al.	28	Res-UNet	RME	MAE
2021	Perera and De Silva	29	LSTM	GFS	Total variation + error variation
Park et al.	30	GAN	RDR	MAE + adversarial loss
Zhou et al.	31	UNet	RDR	MAE + residues
2022	Xu et al.	32	MNet	RME	MAE and MS-SSIM
Zhou et al.	33	GAN	RDR	MAE + adversarial loss
dWC	2018	Liang et al.	34	—	—	—
Spoorthi et al.	35	SegNet	GFS	CE
2019	Zhang et al.	36	UNet	ZPS	CE
Zhang et al.	37	DeepLab-V3+	ZPS	CE
2020	Wu et al.	38	FRRes-UNet	GFS	CE
Spoorthi et al.	39	Dense-UNet	GFS	MAE + residues + CE
Zhao et al.	40	RAENet	ZPS	CE
2021	Zhu et al.	41	DeepLab-V3+	ZPS	CE
2022	Vengala et al.	42,43	TriNet	GSF	MSE + CE
Zhang and Li	44	EESANet	GSF	Weighted CE
dDN	2020	Yan et al.	45	ResNet	ZPS	MSE

Table 2. Summary of datasets. “—” indicates “not available.”

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Table 2. Summary of datasets. “—” indicates “not available.”


Datasets	Size	Proportion of $h$ from 10 to 30	Proportion of $h$ from 30 to 35	Proportion of $h$ from 35 to 40
Training part of D_RME	20,000	50%	20%	30%
Testing part of D_RME	2000	2/3	1/6	1/6
Training part of D_GSF	20,000	50%	20%	30%
Testing part of D_GSF	2000	2/3	1/6	1/6
Training part of D_ZPS	20,000	50%	20%	30%
Testing part of D_ZPS	2,000	2/3	1/6	1/6
D_RDR for testing	421	—	—	—

Table 3. RMSEm, RMSEsd, and PFS of phase unwrapping results of RME-Net, GFS-Net, and ZPS-Net.

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Table 3. RMSEm, RMSEsd, and PFS of phase unwrapping results of RME-Net, GFS-Net, and ZPS-Net.


		D_RME	D_GFS	D_ZPS	D_RDR
${RMSE}_{m}$	RME-Net	0.0910	0.0982	0.1336	0.1103
GSF-Net	0.2263	0.0985	0.1133	0.1184
ZPS-Net	2.5148	0.4221	0.0821	0.8245
${RMSE}_{sd}$	RME-Net	0.0507	0.1037	0.2320	0.1003
GSF-Net	0.4571	0.0234	0.1077	0.1557
ZPS-Net	2.8249	0.6252	0.0220	1.1405
PFS	RME-Net	0.0010	0.0085	0.1270	0.0594
GSF-Net	0.1485	0.0020	0.0560	0.0333
ZPS-Net	0.6525	0.4075	0.0010	0.4679

Table 4. Summary of networks and corresponding datasets. The form of the dataset is {Input, GT}. The last letter of the network name is the case (“I” for ideal, “N” for noisy, “D” for discontinuous, “A” for aliasing, and “M” for mixed).

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Table 4. Summary of networks and corresponding datasets. The form of the dataset is {Input, GT}. The last letter of the network name is the case (“I” for ideal, “N” for noisy, “D” for discontinuous, “A” for aliasing, and “M” for mixed).


Cases	Datasets	Networks	Loss functions
Ideal case (Sec. 4.2)	${φ, ψ}$	dRG-I	MAE
${φ, k}$	dWC-I	CE + MAE
Noisy case (Sec. 4.3)	${φ_{n}, ψ}$	dRG-N	MAE
${φ_{n}, k}$	dWC-N	CE+MAE
{ $R_{n}$ and $I_{n}, R$ and $I$ }	dDN-N	MAE
Discontinuous case (Sec. 4.4)	${φ_{d}, ψ_{d}}$	dRG-D	MAE
${φ_{d}, k_{d}}$	dWC-D	CE + MAE
Aliasing case (Sec. 4.5)	${φ_{a}, ψ_{a}}$	dRG-A	MAE
${φ_{a}, k_{a}}$	dWC-A	CE + MAE
Mixed case (Sec. 4.6)	${φ_{m}, ψ_{m}}$	dRG-M	MAE
${φ_{m}, k_{m}}$	dWC-M	CE + MAE

Table 5. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the ideal case. “-C” represents the congruence results.
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Table 5. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the ideal case. “-C” represents the congruence results.
dRG-I dRG-I-C dWC-I
${RMSE}_{m}$ 0.0989 0.0005 0.0008
${RMSE}_{sd}$ 0.0515 0.0157 0.0251
PFS 0.0015 0.0015 0.0025
PIP 0.0044 0.0044 0.0054

Table 6. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “-C” represents the congruence results.
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Table 6. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “-C” represents the congruence results.
dRG-N (GT) dRG-N-C (GT1) dWC-N (GT1) dDN-N (GT) dDN-N-C (GT1)
${RMSE}_{m}$ 0.1367 0.0285 0.0435 0.0883 0.0229
${RMSE}_{sd}$ 0.1154 0.1148 0.1197 0.2915 0.3056
PFS 0.2525 0.2525 0.2840 0.1976 0.1976
PIP 0.0013 0.0013 0.0014 0.0108 0.0088

Table 7. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the discontinuous case. “-C” represents the congruence results.

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Table 7. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the discontinuous case. “-C” represents the congruence results.


	dRG-I	dRG-D	dRG-D-C	dWC-I	dWC-D	Line-scanning	LS	QG
${RMSE}_{m}$	2.0230	0.1230	0.0261	1.2209	0.0219	3.8054	1.3655	2.4204
${RMSE}_{sd}$	1.7817	0.1636	0.1827	1.3777	0.1543	3.7172	1.0408	2.5014
PFS	0.8120	0.0770	0.0770	0.7385	0.0785	0.9405	0.7120	0.8565
PIP	0.2407	0.0112	0.0112	0.1128	0.0077	0.4400	0.1073	0.2789

Table 8. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the aliasing case. “-C” represents the congruence results.
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Table 8. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the aliasing case. “-C” represents the congruence results.
dRG-A dRG-A-C dWC-A Line-scanning LS QG
${RMSE}_{m}$ 0.1958 0.0078 0.0107 40.5128 6.7199 39.8846
${RMSE}_{sd}$ 0.1390 0.1503 0.1612 21.0695 3.1294 23.0389
PFS 0.0075 0.0075 0.0120 0.9820 0.9895 0.9895
PIP 0.0765 0.0765 0.0467 0.9102 0.5705 0.8369

Table 9. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the mixed case. “-C” represents the congruence results.
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Table 9. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the mixed case. “-C” represents the congruence results.
dRG-M dRG-M-C dWC-M Line-scanning LS QG
${RMSE}_{m}$ 0.2362 0.1266 0.2206 38.4389 10.8350 39.4653
${RMSE}_{sd}$ 0.3101 0.3790 0.4618 21.0695 3.6269 18.1084
PFS 0.3740 0.3740 0.4810 1.0000 1.0000 1.0000
PIP 0.0106 0.0106 0.0107 0.9569 0.7600 0.9107

Table 10. Performance statistics in the ideal, noisy, discontinuous, and aliasing cases. “✓” represents “capable.” “✓✓” represents “best and recommended.” “✗” represents “incapable.” “—” indicates “not applicable.”

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Table 10. Performance statistics in the ideal, noisy, discontinuous, and aliasing cases. “✓” represents “capable.” “✓✓” represents “best and recommended.” “✗” represents “incapable.” “—” indicates “not applicable.”


Cases	dRG	dWC	dDN	Line-scanning	LS	QG	WFT-QG
Ideal	✓	✓	✓	✓✓	✓	✓	—
Slight noise	✓	✓	✓	✓	✓	✓	✓
Moderate noise	✓✓	✓✓	✓	✗	✗	✗	✓✓
Severe noise	✓✓	✓✓	✓	✗	✗	✗	✓✓
Discontinuity	✓✓	✓✓	—	✗	✗	✗	—
Aliasing	✓✓	✓✓	—	✗	✗	✗	—
Mixed	✓✓	✓✓	—	✗	✗	✗	—

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Kaiqiang Wang, Qian Kemao, Jianglei Di, Jianlin Zhao, "Deep learning spatial phase unwrapping: a comparative review," Adv. Photon. Nexus 1, 014001 (2022)

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Paper Information

Category: Reviews

Received: Jun. 22, 2022

Accepted: Jun. 28, 2022

Published Online: Aug. 4, 2022

The Author Email: Kemao Qian (mkmqian@ntu.edu.sg), Di Jianglei (jiangleidi@nwpu.edu.cn), Zhao Jianlin (jlzhao@nwpu.edu.cn)

DOI:10.1117/1.APN.1.1.014001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Summary of deep-learning-involved phase unwrapping methods. “—” indicates “not available.”

Table 1. Summary of deep-learning-involved phase unwrapping methods. “—” indicates “not available.”

Table 2. Summary of datasets. “—” indicates “not available.”

Table 2. Summary of datasets. “—” indicates “not available.”

Table 3. RMSEm, RMSEsd, and PFS of phase unwrapping results of RME-Net, GFS-Net, and ZPS-Net.

Table 3. RMSEm, RMSEsd, and PFS of phase unwrapping results of RME-Net, GFS-Net, and ZPS-Net.

Table 4. Summary of networks and corresponding datasets. The form of the dataset is {Input, GT}. The last letter of the network name is the case (“I” for ideal, “N” for noisy, “D” for discontinuous, “A” for aliasing, and “M” for mixed).

Table 4. Summary of networks and corresponding datasets. The form of the dataset is {Input, GT}. The last letter of the network name is the case (“I” for ideal, “N” for noisy, “D” for discontinuous, “A” for aliasing, and “M” for mixed).

Table 5. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the ideal case. “-C” represents the congruence results.

Table 5. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the ideal case. “-C” represents the congruence results.

Table 6. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “-C” represents the congruence results.

Table 6. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved methods in the noisy case. “GT” represents the pure GT (pure absolute phase), while “GT1” represents the noisy GT (noisy absolute phase). “-C” represents the congruence results.

Table 7. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the discontinuous case. “-C” represents the congruence results.

Table 7. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the discontinuous case. “-C” represents the congruence results.

Table 8. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the aliasing case. “-C” represents the congruence results.

Table 8. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the aliasing case. “-C” represents the congruence results.

Table 9. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the mixed case. “-C” represents the congruence results.

Table 9. RMSEm, RMSEsd, PFS, and PIP of the deep-learning-involved and traditional methods in the mixed case. “-C” represents the congruence results.

Table 10. Performance statistics in the ideal, noisy, discontinuous, and aliasing cases. “✓” represents “capable.” “✓✓” represents “best and recommended.” “✗” represents “incapable.” “—” indicates “not applicable.”

Table 10. Performance statistics in the ideal, noisy, discontinuous, and aliasing cases. “✓” represents “capable.” “✓✓” represents “best and recommended.” “✗” represents “incapable.” “—” indicates “not applicable.”

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