Acta Optica Sinica, Volume. 43, Issue 5, 0507001(2023)
Fourier Transform Profilometry Based on Improved Goldstein Branch-Cut Algorithm
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Fig. 2. Diagrammatic sketch of improved Goldstein branch-cut algorithm, the numbers represent weights of edges. (a) Example of weighted bipartite graph; (b) example of perfect matching
Fig. 3. Measured object, deformed fringe pattern, and wrapped phase map. (a) Measured object; (b) deformed fringe pattern; (c) wrapped phase map
Fig. 4. Distribution of residues and branch-cuts. (a) Residues distribution; (b) branch-cuts obtained by Goldstein branch-cut algorithm; (c) branch-cuts obtained by proposed algorithm
Fig. 5. Contrast results. (a) Reconstructed result obtained by flood-fill algorithm; (b) reconstructed result obtained by Goldstein branch-cut algorithm; (c) reconstructed result obtained by proposed algorithm
Fig. 7. Fringe patterns. (a) Reference fringe pattern; (b) deformed fringe pattern
Fig. 8. Wrapped phase map and reconstructed result obtained by flood-fill algorithm. (a) Wrapped phase map; (b) reconstructed result
Fig. 9. Distribution of residues and branch-cuts. (a) Residues distribution; (b) branch-cuts obtained by Goldstein branch-cut algorithm; (c) branch-cuts obtained by proposed algorithm
Fig. 10. Contrast results. (a) Reconstructed result obtained by Goldstein branch-cut algorithm; (b) reconstructed result obtained by proposed algorithm
Fig. 11. Reconstruction experiment of donkey face model. (a) Donkey face model; (b) deformed fringe pattern; (c) wrapped phase map; (d) branch-cuts obtained by Goldstein branch-cut algorithm; (e) branch-cuts obtained by proposed algorithm; (f) reconstructed result obtained by flood-fill algorithm; (g) reconstructed result obtained by Goldstein branch-cut algorithm; (h) reconstructed result obtained by proposed algorithm
Fig. 12. Reconstruction experiment results of bear. (a) Deformed fringe pattern; (b) wrapped phase map; (c) branch-cuts obtained by Goldstein branch-cut algorithm; (d) branch-cuts obtained by proposed algorithm; (e) reconstructed result obtained by Goldstein branch-cut algorithm; (f) reconstructed result obtained by proposed algorithm
Table 1. Comparison of RMSE, length of branch-cuts, and time for the various algorithms
View tableTable 1. Comparison of RMSE, length of branch-cuts, and time for the various algorithms
Algorithm Length of branch-cuts /pixel RMSE /mm Time /s Goldstein branch-cut algorithm 239 0.6329 0.0674 Proposed algorithm 89 0.4041 0.0378
Table 2. RMSE of Goldstein branch-cut algorithm and proposed algorithm under different noises
View tableTable 2. RMSE of Goldstein branch-cut algorithm and proposed algorithm under different noises
Algorithm RMSE /mm Gaussian noise with a standard deviation 1 Gaussian noise with a standard deviation 3 Gaussian noise with a standard deviation 5 Goldstein branch-cut algorithm 0.0677 0.6329 1.6118 Proposed algorithm 0.0677 0.4041 0.8070
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Qian You, Hui Weng, Jiang Zhao, Yuebin Li, Wenfeng Wang, Shi Lu, Kuang Peng. Fourier Transform Profilometry Based on Improved Goldstein Branch-Cut Algorithm[J]. Acta Optica Sinica, 2023, 43(5): 0507001
Paper Information
Category: Fourier optics and signal processing
Received: Jun. 20, 2022
Accepted: Oct. 14, 2022
Published Online: Mar. 13, 2023
The Author Email: Peng Kuang (pengkuang91@163.com)
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