Surface Grid Calibration of Line Structured Light Based on Ray-Tracing

Xiaoqian Wang; Kun Xu; Shoucang Wu; Tao Peng; Zhenzhen Huang; Zhijiang Zhang

doi:10.3788/AOS231544

Acta Optica Sinica, Volume. 44, Issue 2, 0212004(2024)

Surface Grid Calibration of Line Structured Light Based on Ray-Tracing

Xiaoqian Wang¹, Kun Xu², Shoucang Wu², Tao Peng¹, Zhenzhen Huang¹, and Zhijiang Zhang^1、*

¹Key Laboratory of Specialty Fiber Optics and Optical Access Networks, School of Communication & Information Engineering, Shanghai University, Shanghai 200444, China

²MCC Baosteel Technology Service Co. Ltd., Shanghai 201999, China

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Figures & Tables(20)

Fig. 1. Line structured light vision system

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Fig. 2. Schematic diagram of horizontal ray-tracing. (a) Curved light surface; (b) camera ray plane

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Fig. 3. Line structured light imaging geometry model

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Fig. 4. Schematic diagram of line structured light surface grid

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Fig. 5. Intersecting grid points

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Fig. 6. Subpixel light strip center point

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Fig. 7. Calibration system flow chart

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Fig. 8. Field of line structured light surface calibration experiment

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Fig. 9. Polynomial fitting results. (a) Horizontal ray-tracing; (b) vertical ray-tracing

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Fig. 10. Local results of the ray-tracing grid

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Fig. 11. Calibration plane reconstruction with error distribution. (a1) (a2) Proposed method; (b1) (b2) LPM; (c1) (c2) PFC

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Fig. 12. Results of distance measurement

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Table 1. Camera calibration parameters
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Table 1. Camera calibration parameters
Parameter name Result
f_x，f_y 3479.8270，3480.1814
u₀，v₀ 2536.5745，2621.4617
k₁，k₂，k₃ -0.07170，0.08888，-0.02706
p₁，p₂ 0.00114，0.00015

Table 2. Polynomial fitting results of different orders

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Table 2. Polynomial fitting results of different orders

Method		Order of polynomial
Method		2	3	4	5	6
RMSE S /mm	Horizontal ray-tracing	8.647	1.841	1.208	10.754	30.661
RMSE S /mm	Vertical ray-tracing	3.304	0.585	0.395	0.384	0.527
Time T /s	Horizontal ray-tracing	1.365	1.282	1.282	1.287	1.218
Time T /s	Vertical ray-tracing	0.343	0.283	0.315	0.300	0.276
Number of polynomials N_P	Horizontal ray-tracing	2005	1955	1924	1899	1861
Number of polynomials N_P	Vertical ray-tracing	562	506	495	481	459

Table 3. Calibration results with different number of calibration images

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Table 3. Calibration results with different number of calibration images

Method		Number of calibration images
Method		40	30	20	15	10
Mean error E /mm	HRT	0.764	0.670	0.587	0.670	0.582
	VRT	0.291	0.290	0.228	0.266	0.347
	Proposed method	0.678	0.601	0.524	0.592	0.548
Number of sample points N_S	HRT	43748	31932	20061	10366	4350
	VRT	9725	7105	4328	2490	739
	Proposed method	53473	39037	24389	12856	5089
Number of polynomials N_P	HRT	1924	1876	1621	1043	558
	VRT	495	466	402	265	100
	Proposed method	2419	2342	2023	1308	658

Table 4. Calibration accuracies of Gaussian noise with different mean values

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Table 4. Calibration accuracies of Gaussian noise with different mean values

Method	Without noise	Mean value of Gaussian noise $μ_{G}$
Method	Without noise	2	4	6	8	10
HRT	0.764	0.733	0.749	0.732	0.732	0.747
VRT	0.291	0.265	0.285	0.265	0.263	0.284
Proposed method	0.678	0.648	0.664	0.646	0.646	0.662
LPM	0.126	0.125	0.127	0.125	0.125	0.127
PFC	38.275	38.710	38.277	38.714	38.712	38.279

Table 5. Calibration accuracies of Gaussian noise with different standard deviations

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Table 5. Calibration accuracies of Gaussian noise with different standard deviations

Method	Without noise	Standard deviation of Gaussian noise $σ_{G}$
Method	Without noise	5	10	15	20
HRT	0.764	0.732	0.733	0.732	0.747
VRT	0.291	0.264	0.264	0.263	0.284
Proposed method	0.678	0.646	0.647	0.646	0.662
LPM	0.126	0.125	0.125	0.125	0.127
PFC	38.275	38.711	38.715	38.714	38.279

Table 6. Accuracies of plate measurement

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Table 6. Accuracies of plate measurement

Distance D_P /mm	Method	Number of calibration images
Distance D_P /mm	Method	40 planer targets	30 planer targets	20 planer targets	15 planer targets	10 planer targets
1294.47	Proposed method	0.520	0.518	0.523	0.638	—
	LPM	0.571	0.630	0.624	0.544	—
	PFC	3.768	9.863	20.815	50.740	—
1589.78	Proposed method	0.835	0.832	0.897	0.987	0.820
	LPM	0.889	0.924	1.045	1.286	1.266
	PFC	34.382	27.744	35.074	22.608	25.357
1693.48	Proposed method	0.996	0.993	0.999	1.023	0.979
	LPM	1.134	1.140	1.203	1.630	1.596
	PFC	18.589	6.764	12.296	16.512	15.035
1767.24	Proposed method	0.959	1.079	1.065	1.148	1.016
	LPM	1.134	1.085	1.121	1.543	1.362
	PFC	6.331	7.973	4.441	9.263	7.340

Table 7. Accuracies of distance measurement

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Table 7. Accuracies of distance measurement

Method	Distance to be measured
Method	d₁/mm	d₂/mm	d₃/mm	d₄/mm	d_H/mm	d_V/mm
HRT	0.017	1.139	0.177	0.744	0.030	0.046
VRT	0.806	0.026	0.471	0.064	0.024	0.034
Proposed method	0.399	0.280	0.340	0.354	0.028	0.030
LPM	0.113	1.059	0.151	0.604	0.027	0.038
PFC	3.575	8.501	6.952	1.001	0.493	0.202

Table 8. Measurement accuracies of standard body size unit: mm
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Table 8. Measurement accuracies of standard body size unit: mm
Method HRT VRT Proposed method LPM PFC
Length 0.479 0.145 0.025 0.457 6.643
Width 0.327 0.480 0.062 0.187 1.386

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Xiaoqian Wang, Kun Xu, Shoucang Wu, Tao Peng, Zhenzhen Huang, Zhijiang Zhang. Surface Grid Calibration of Line Structured Light Based on Ray-Tracing[J]. Acta Optica Sinica, 2024, 44(2): 0212004

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