Background Removal of Fringe Projection Patterns Based on Modified Fuzzy c-Means Clustering Algorithm

Qi Zhao; Chen Tang; Min Xu; Zhenkun Lei

doi:10.3788/LOP202259.2411002

Laser & Optoelectronics Progress, Volume. 59, Issue 24, 2411002(2022)

Background Removal of Fringe Projection Patterns Based on Modified Fuzzy c-Means Clustering Algorithm

Qi Zhao¹, Chen Tang^1、*, Min Xu¹, and Zhenkun Lei²

Author Affiliations

¹School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China

²State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning, China

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Figures & Tables(6)

Fig. 1. Results comparison of first simulated fringe projection pattern. (a) Original fringe projection pattern; (b)-(d) Fig.1(a) corresponding theoretical background, fringe, and unwrapped phase; (b1)-(d1)corresponding results of FT on background, fringe, and unwrapped phase; (b2)-(d2) corresponding results of MOBEMD on background, fringe, and unwrapped phase; (b3)-(d3) corresponding results of TV-Hilbert-L² on background, fringe, and unwrapped phase; (b4)-(d4) corresponding results of proposed method on background, fringe, and unwrapped phase; (e)-(e4) enlarged details corresponding to Fig.1(d)-(d4)

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Fig. 2. Results comparison of second simulated fringe projection pattern. (a) Original fringe projection pattern; (b)-(d) Fig.2(a) corresponding theoretical background, fringe, and unwrapped phase; (b1)-(d1) corresponding results of FT on background, fringe, and unwrapped phase; (b2)-(d2) corresponding results of MOBEMD on background, fringe, and unwrapped phase; (b3)-(d3) corresponding results of TV-Hilbert-L² on background, fringe, and unwrapped phase; (b4)-(d4) corresponding results of proposed method on background, fringe, and unwrapped phase; (e)-(e4) enlarged details corresponding to Fig.2(d)-(d4)

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Fig. 3. Results comparison of experimental fringe projection pattern. (a) Original fringe projection pattern; (b) corresponding theoretical unwrapped phase; (c1)-(e1) corresponding results of FT on background, fringe, and unwrapped phase; (c2)-(e2) corresponding results of MOBEMD on background, fringe, and unwrapped phase; (c3)-(e3) corresponding results of TV-Hilbert-L² on background, fringe, and unwrapped phase; (c4)-(e4) corresponding results of proposed method on background, fringe, and unwrapped phase

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Fig. 4. Results comparison of noise performance test. (a) Original fringe projection pattern; (b) corresponding theoretical fringe; (c)-(g) fringe patterns obtained by proposed method after adding 0.2, 0.4, 0.8, 1, 1.2 Gaussian random noise respectively

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Table 1. Evaluation metrics on results for simulated fringe projection patterns

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Table 1. Evaluation metrics on results for simulated fringe projection patterns

Fringe projection pattern	Method	$S N R_{F}$ /dB	$M S E_{p}$
Fig. 1	FT	6.93	2.36×10^-7
	MOBEMD	9.51	1.39×10^-7
	TV-Hilbert-L²	14.93	3.68×10^-9
	Proposed method	16.53	2.63×10^-⁹
Fig. 2	FT	10.52	8.63×10^-7
	MOBEMD	11.14	1.17×10^-8
	TV-Hilbert-L²	16.49	3.10×10^-9
	Proposed method	16.82	2.66×10^-⁹

Table 2. Evaluation metrics on results for experimental fringe projection pattern
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Table 2. Evaluation metrics on results for experimental fringe projection pattern
Fringe projection pattern Method $M S E_{p}$
Fig. 3 FT 1.63×10^-6
MOBEMD 4.25×10^-7
TV-Hilbert-L² 3.02×10^-7
Proposed method 2.11×10^-⁷

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Qi Zhao, Chen Tang, Min Xu, Zhenkun Lei. Background Removal of Fringe Projection Patterns Based on Modified Fuzzy c-Means Clustering Algorithm[J]. Laser & Optoelectronics Progress, 2022, 59(24): 2411002

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