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High-speed three-dimensional shape measurement based on cyclic complementary Gray-code light

Zhoujie Wu, Chao Zuo, Wenbo Guo, Tianyang Tao, and Qican Zhang

Open Access Open Access

Abstract

The binary defocusing technique has been widely used in high-speed three-dimensional (3D) shape measurement because it breaks the bottlenecks in high-speed fringe projection and the projector’s nonlinear response. However, it is challenging for this method to realize a two- or multi-frequency phase-shifting algorithm because it is difficult to simultaneously generate high-quality sinusoidal fringe patterns with different periods under the same defocusing degree. To bypass this challenge, we proposed a high-speed 3D shape measurement technique for dynamic scenes based on cyclic complementary Gray-code (CCGC) patterns. In this proposed method, the projected phase-shifting sinusoidal fringes kept one same frequency, which is beneficial to ensure the optimum defocusing degree for binary dithering technique. The wrapped phase can be calculated by phase-shifting algorithm and unwrapped with the aid of complementary Gray-code (CGC) patterns in a simple and robust way. Then, the cyclic coding strategy further extends the unambiguous phase measurement range and improves the measurement accuracy compared with the traditional Gray-coding strategy under the condition of the same number of projected patterns. High-quality 3D results of three complex dynamic scenes—including a cooling fan and a standard ceramic ball with a free-falling table tennis, collapsing building blocks, and impact of the Newton’s cradle—were demonstrated at a frame rate of 357 fps. This verified the proposed method’s feasibility and validity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Supplementary Material (3)

NameDescription
Visualization 1       Visualization 1
Visualization 2       Visualization 2
Visualization 3       Visualization 3

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Figures (12)
Figure 1
Figure 1 Sketch map of complementary Gray-code method. (a)-(c) Phase-shifting dithered patterns. (d) The wrapped phase. (e)-(g) Traditional Gray-code patterns. (h) The additional Gray-code pattern.

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Fig. 2
Fig. 2 Sketch map of cyclic coding strategy of complementary Gray-code light. (a)-(c) Phase-shifting dithered patterns in pattern sequence n-1. (d)-(g) Cyclic complementary Gray-code patterns (CCP) in pattern sequence n-1. (h)-(n) Corresponding patterns in pattern sequence n. (o) CCP1 in pattern sequence n-1. (p) Uncorrected CCP1 in pattern sequence n. (q) Phase order k3. (r) Corrected CCP1 in pattern sequence n.

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Fig. 3
Fig. 3 The obtainment of phase orders k1, k2 and k3.

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Fig. 4
Fig. 4 Error caused by binarization and motion. (a) CCP1 in sequence n-1. (b) Uncorrected CCP1 in sequence n. (c) Phase order k3 with errors in sequence n. (d) Corrected CCP1 with errors in sequence n. (e) CCP4 in sequence n. (f) Phase order k2 with errors in sequence n. (g) Phase order k1 with errors in sequence n.

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Fig. 5
Fig. 5 Correction of the phase-jump errors in phase-to-height mapping process. (a) Phase-to-height mapping space. (b) The middle cross-section of (a).

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Fig. 6
Fig. 6 Photograph of the high-speed 3D shape measurement system.

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Fig. 7
Fig. 7 Continuously captured fringe images for three methods (Visualization 1). (a) A sequence of 8 continuous fringe images for the GC and CGC methods. (b) Seven continuous fringe images for the CCGC method in sequence n-1. (c) Seven continuous fringe images for the CCGC method in sequence n.

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Fig. 8
Fig. 8 Data processing and accuracy analyzing of the CCGC method. (a) Test scene consisting of a cooling fan for CPU, a standard ceramic ball and a free-falling table tennis at T = 100ms. (b) Uncorrected absolute phase. (c)-(d) One cross-section (highlighted in (b)) of the uncorrected absolute phase. (e) Corrected absolute phase. (f) Reconstructed result. (g) Sphere fitting of the table tennis in (f). (h) Sphere fitting of the standard ceramic ball in (f). (i) Error distribution of the measured table tennis. (j) Error distribution of the measured standard ceramic ball.

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Fig. 9
Fig. 9 Comparative assessment of GC, CGC and CCGC methods.

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Fig. 10
Fig. 10 Measurement of collapsing building blocks. (a) Representative collapsing scenes at different time points. (b) Corresponding 3D reconstructions (Visualization 2).

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Fig. 11
Fig. 11 Measurement of the impact process of the Newton’s cradle. (a) Representative scenes at different time points. (b) Corresponding 3D reconstructions (Visualization 3). (c) The 3D point cloud of the scene at the first moment, with the color line showing the trajectory and velocity of the left and right ball. (d) The velocity profile of the left and right balls. (e) Different postures of the balls at the corresponding moments in (d).

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Fig. 12
Fig. 12 Evaluation of the maximum measuring velocity in the perpendicular direction of the fringe direction. (a) Unwrapping phase of the fourth reference. (b) The derivative of distance in X-axis to phase in the middle row of (a).

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Equations (14)

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I 1 ( x , y , n ) = α ( x , y , n ) { a p + b p cos [ ϕ ( x , y , n ) − 2 π / 3 ] + β 1 ( x , y , n ) } + β 2 ( x , y , n )
I 2 ( x , y , n ) = α ( x , y , n ) { a p + b p cos [ ϕ ( x , y , n ) ] + β 1 ( x , y , n ) } + β 2 ( x , y , n )
I 3 ( x , y , n ) = α ( x , y , n ) { a p + b p cos [ ϕ ( x , y , n ) + 2 π / 3 ] + β 1 ( x , y , n ) } + β 2 ( x , y , n )
ϕ ( x , y , n ) = tan − 1 3 ( I 1 ( x , y , n ) − I 3 ( x , y , n ) ) 2 I 2 ( x , y , n ) − I 1 ( x , y , n ) − I 3 ( x , y , n )
k 3 ( x , y , n ) = C C P 1 ( x , y , n ) ⊕ C C P 1 ( x , y , n − 1 )
C C P 1 ( x , y , n ) = ( mod ( n + 1 , 2 ) * k 3 ( x , y , n ) ) ⊕ C C P 1 ( x , y , n )
V 1 ( x , y , n ) = ∑ i = 1 3 C C P i ( x , y , n ) * 2 ( 3 − i )
V 2 ( x , y , n ) = ∑ i = 1 4 C C P i ( x , y , n ) * 2 ( 4 − i )
k 2 ( x , y , n ) = I N T ( ( i ( V 2 ( x , y , n ) ) + 1 ) / 2 )
Φ ( x , y , n ) = { ϕ ( x , y , n ) + 2 π ( k 2 ( x , y , n ) + 8 k 3 ( x , y , n ) ) , ϕ ( x , y , n ) ≤ - π / 2 ϕ ( x , y , n ) + 2 π ( k 1 ( x , y , n ) + 8 k 3 ( x , y , n ) ) , - π / 2 < ϕ ( x , y , n ) < π / 2 ϕ ( x , y , n ) + 2 π ( k 2 ( x , y , n ) + 8 k 3 ( x , y , n ) ) - 2 π , ϕ ( x , y , n ) ≥ π / 2 .
1 h ( x , y , n ) = u ( x , y ) + v ( x , y ) Δ Φ ( x , y , n ) + w ( x , y ) Δ Φ 2 ( x , y , n ) ,
Δ Φ ( x , y , n ) = { Δ Φ ( x , y , n ) − 16 π , Δ Φ ( x , y , n ) > Φ 1 Δ Φ ( x , y , n ) + 16 π , Δ Φ ( x , y , n ) < Φ 2
V Z max = h min r / m .
V X max = d min r / m .
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