Fringe Order Correction for Fringe Projection Profilometry Based on Robust Principal Component Analysis

Temporal phase unwrapping is among the most robust and efficient phase unwrapping methods in fringe projection profilometry. They can recover the fringe orders even in the presence of surface discontinuities. However, fringe order errors may occur due to phase noise and poor measurement conditions. Such errors often exhibit an impulsive nature and introduce errors to the absolute phase map. Most existing fringe order error correction methods detect and correct the errors in a pixel-by-pixel manner, which may under-utilize the correlation of the fringe orders on different pixels. In this paper, we propose a new method to cope with the fringe order errors associated with temporal phase unwrapping. By exploiting the low-rankness of the fringe order map and sparse nature of the impulsive fringe order errors, we develop a robust principal component analysis (RPCA)-based approach to remove the impulsive fringe order errors. Experiments demonstrate that the proposed method is valid in eliminating the fringe order errors.

[1]  H. Andrews,et al.  Singular value decompositions and digital image processing , 1976 .

[2]  Lu Zhang,et al.  Fringe order error in multifrequency fringe projection phase unwrapping: reason and correction. , 2015, Applied optics.

[3]  Chao Zuo,et al.  Automatic identification and removal of outliers for high-speed fringe projection profilometry , 2013 .

[4]  Soon Ki Jung,et al.  Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset , 2015, Comput. Sci. Rev..

[5]  Song Zhang.  Recent progresses on real-time 3D shape measurement using digital fringe projection techniques , 2010 .

[6]  Seah Hock Soon,et al.  Valid point detection in fringe projection profilometry. , 2015, Optics express.

[7]  Zonghua Zhang,et al.  Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques , 2012 .

[8]  Qican Zhang,et al.  Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies. , 2011, Applied optics.

[9]  Lei Huang,et al.  Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review , 2016 .

[10]  Yi Ding,et al.  Recovering the absolute phase maps of two fringe patterns with selected frequencies. , 2011, Optics letters.

[11]  Dongliang Zheng,et al.  Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter. , 2017, Optics express.

[12]  Qian Chen,et al.  Phase shifting algorithms for fringe projection profilometry: A review , 2018, Optics and Lasers in Engineering.

[13]  A. Asundi,et al.  Phase invalidity identification framework with the temporal phase unwrapping method , 2011 .

[14]  Rong Mo,et al.  Invalid phase values removal method for absolute phase recovery. , 2016, Applied optics.

[15]  Xiaoming Yuan,et al.  Sparse and low-rank matrix decomposition via alternating direction method , 2013 .

[16]  Hong Zhao,et al.  Fringe-period selection for a multifrequency fringe-projection phase unwrapping method , 2016 .

[17]  Thierry Bouwmans,et al.  Robust PCA via Principal Component Pursuit: A review for a comparative evaluation in video surveillance , 2014, Comput. Vis. Image Underst..

[18]  Yi Ding,et al.  Absolute phase recovery of three fringe patterns with selected spatial frequencies , 2015 .

[19]  Song Zhang,et al.  Absolute phase retrieval methods for digital fringe projection profilometry: A review , 2018 .

[20]  Pablo A. Parrilo,et al.  Rank-Sparsity Incoherence for Matrix Decomposition , 2009, SIAM J. Optim..

[21]  Jiangtao Xi,et al.  Frequency selection in absolute phase maps recovery with two frequency projection fringes. , 2012, Optics express.

[22]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[23]  Jiangtao Xi,et al.  Recovery of absolute phases for the fringe patterns of three selected wavelengths with improved anti-error capability , 2016 .

[24]  Ziqi Zhu,et al.  Simplified fringe order correction for absolute phase maps recovered with multiple-spatial-frequency fringe projections , 2017 .

[25]  Song Zhang,et al.  Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm , 2009 .

[26]  Jiangtao Xi,et al.  Error analysis in the absolute phase maps recovered by fringe patterns with three different wavelengths , 2018 .