Parallel optimization of tridimensional deformation measurement based on correlation function constraints of a multi-camera network

Guiyang Zhang; Guiyang Zhang; Guiyang Zhang; Liang Wei; Bin Zhang; Bin Zhang; Xing Zhou; Ju Huo

doi:10.1364/AO.471747

Applied Optics
Vol. 61,
Issue 32,
pp. 9311-9323
(2022)
•https://doi.org/10.1364/AO.471747

Parallel optimization of tridimensional deformation measurement based on correlation function constraints of a multi-camera network

Guiyang Zhang, Liang Wei, Bin Zhang, Xing Zhou, and Ju Huo

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Guiyang Zhang, Liang Wei, Bin Zhang, Xing Zhou, and Ju Huo, "Parallel optimization of tridimensional deformation measurement based on correlation function constraints of a multi-camera network," Appl. Opt. 61, 9311-9323 (2022)

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- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: July 27, 2022
- Revised Manuscript: September 25, 2022
- Manuscript Accepted: October 3, 2022
- Published: October 25, 2022

Abstract

This study primarily investigates the low accuracy and redundant time-consuming problem of speckle registration in the full-field deformation measurement of slender and biggish specimens. To solve these problems, a parallel optimization of the tridimensional deformation measurement method is proposed based on what we believe is a novel correlation function constraints of a multi-camera network. First, a neotype correlation function is built based on the joint constraint relationship among the multiple cameras, which is capable of accurately restricting the search for homologous points in image pairs to the epipolar line, instead of the entire image, while significantly narrowing the search space and accelerating the search. The multiple cameras are bundled as a whole, thus reducing the dimension of the Jacobian matrix and the normalized matrix to a certain extent. Subsequently, more speckle images can be calculated in one iteration. Furthermore, the decomposition of the derived correlation function and the scheme of the parallel algorithm are decomposed via the kernel function based on the GPU parallel mechanism of the compute unified device architecture source program, thus increasing the subpixel search speed of speckle matching and ensuring the calculation performance of the stereo deformation measurement method to reach a higher level. Lastly, the experimental results revealed that the proposed strategy could allow the calculation speed-up ratio of speckle sequence and stereo registration to reach 20.390 times and 17.873 times, respectively, while ensuring the out-of-plane displacement average measuring accuracy to be higher than 0.179 mm within the spatial range of [2 m, 2 m, 3 m]. As a result, the proposed approach has crucial applications in rapid and stable tridimensional deformation measurement.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Step 1:	Input thread number, reference image, and deformed image sequence, and define registration matrix space and calibration matrix space.
Step 2:	Download the precalculated data package $k_{0}, e, e_{min}, e_{max}$ .
Step 3:	Define the kernel function thread index and initialize the parallel calculation parameters.
Step 4:	Decompose the $n$ th correlation function, including creating the inverse matrix space of the Hessian matrix, creating the Hessian matrix space, creating the Jacobi matrix space, as well as creating the shape function parameter space.
Step 5:	Iteratively solve the speckle stereo registration based on the correlation function, upon which the parameter vector $\vec{P}$ and the coordinate of the corresponding image speckle point $(x_{i}^{'}, y_{j}^{'})$ can be obtained.
Step 6:	Block threads to ensure thread synchronization.
Step 7:	Free up memory space.
Step 8:	Output sequence and stereo registration data.

		Time Consumed per Point (s)
No.	Number of Points	Based on CPU	Based on CUDA	Speedup Ratio
1	5	14.498	1.804	8.036
2	20	12.436	0.882	14.099
3	50	12.111	0.675	17.942
4	100	11.020	0.603	18.275
5	150	12.111	0.612	19.789
6	200	11.991	0.619	19.371
7	250	12.111	0.612	19.789
8	300	12.336	0.605	20.390

		Time Consumed per Point (s)
No.	Number of Points	Based on CPU	Based on CUDA	Speedup Ratio
1	5	10.424	1.582	6.589
2	20	10.176	0.773	13.155
3	50	10.016	0.592	16.918
4	100	9.921	0.558	17.759
5	150	9.921	0.562	17.644
6	200	9.901	0.561	17.625
7	250	9.920	0.566	17.521
8	300	9.884	0.553	17.873

Intrinsic Parameters	Relative Pose Relationship among Cameras
$f_{u} = 3279 .6214$ $u_{0} = 1043 .7560$ $f_{v} = 3280 .0549$	${\begin{matrix} R_{η 1} = [\begin{matrix} 0.9962 & 0.0204 & - 0.1963 \\ - 0.0189 & 0.9974 & - 0.1036 \\ 0.1200 & 0.0205 & 0.9870 \end{matrix}] \\ t_{η 1} = [- 168.4516 6.9370 - 1.9004]^{T} \end{matrix}$
$v_{0} = 1028.0395$ $k_{1} = - 0 .1492$ $k_{2} = 0.1203$	${\begin{matrix} R_{η 2} = [\begin{matrix} 0.9914 & 0.0265 & - 0.1092 \\ - 0.0250 & 0.9989 & 0.0376 \\ 0.1724 & - 0.0370 & 0.9953 \end{matrix}] \\ t_{η 2} = {[\begin{matrix} - 254.7622 & - 4.2503 & 9.8416 \end{matrix}]}^{T} \end{matrix}$
$γ = 0.0000$ $ρ_{1} = 0.0000$ $ρ_{2} = 0.0000$	${\begin{matrix} R_{η 3} = [\begin{matrix} 0.9899 & 0.0199 & - 0.1704 \\ - 0.0198 & 0.9991 & 0.0193 \\ 0.1602 & - 0.0305 & 0.9890 \end{matrix}] \\ t_{η 3} = {[\begin{matrix} - 391.4856 & 4.0526 & 6.8605 \end{matrix}]}^{T} \end{matrix}$
Physical calibration error	0.135 mm

	Measurement Data by	Error Absolute Value of Different Methods in $z$ Direction (mm)
No.	Total Station	IGGA	Normal-SRPG	ICGN	RJCO
1	8.013	0.262	0.235	0.230	0.153
2	12.574	0.293	0.255	0.266	0.161
3	17.269	0.289	0.261	0.259	0.155
4	20.534	0.298	0.269	0.274	0.178
5	23.360	0.316	0.301	0.296	0.184
6	24.994	0.335	0.308	0.315	0.209
7	24.725	0.338	0.295	0.302	0.215
8	23.931	0.331	0.286	0.278	0.204
9	22.676	0.294	0.271	0.285	0.195
10	21.315	0.312	0.278	0.292	0.186
11	19.826	0.308	0.265	0.268	0.179
12	18.451	0.291	0.260	0.262	0.172
13	16.913	0.296	0.249	0.258	0.167
14	15.184	0.285	0.253	0.261	0.170
15	13.392	0.270	0.257	0.265	0.162
Mean $\| error \|$		0.301	0.269	0.274	0.179
Standard deviation		0.022	0.020	0.021	0.019

Abstract

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Applied Optics