Efficient and automated initial value estimation in digital image correlation for large displacement, rotation, and scaling

Zheng Fang; Yue Gao; Zeren Gao; Yang Liu; Yaru Wang; Yong Su; Yong Su; Qingchuan Zhang

doi:10.1364/AO.405551

Applied Optics
Vol. 59,
Issue 33,
pp. 10523-10531
(2020)
•https://doi.org/10.1364/AO.405551

Efficient and automated initial value estimation in digital image correlation for large displacement, rotation, and scaling

Zheng Fang, Yue Gao, Zeren Gao, Yang Liu, Yaru Wang, Yong Su, and Qingchuan Zhang

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Zheng Fang, Yue Gao, Zeren Gao, Yang Liu, Yaru Wang, Yong Su, and Qingchuan Zhang, "Efficient and automated initial value estimation in digital image correlation for large displacement, rotation, and scaling," Appl. Opt. 59, 10523-10531 (2020)

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Abstract

The initial value estimation for seed point is the first step in digital image correlation calculation. Among the existing algorithms, the Fourier–Mellin transform-based cross correlation (FMT-CC) algorithm is one of the most efficient and robust owing to its rotation- and scale-invariance. However, when the displacement is large (more than a hundred pixels), the FMT-CC algorithm fails. In this paper, an automated and efficient initial value estimation method based on an FMT-CC algorithm is presented to deal with large displacement, large rotation, and large isotropic scaling. The relationship between subset size and the maximal displacement in the FMT-CC algorithm is studied, and a strategy of setting the subset size according to the estimated displacement is proposed to improve the robustness of the FMT-CC algorithm. In addition, in cases of large displacement, a multi-scale search method is proposed to improve efficiency. The experimental results show that the proposed methods can realize rapid and automated initial value estimation even under conditions of large displacement, large rotation, and large isotropic scaling. The computational efficiency of the multi-scale search method is about one order of magnitude higher than the traditional FMT-CC method.

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Experiments	$θ_{0} (^{\circ})$	$s_{0}$	$N (p i x e l)$
1	0, 30, 60, 90, 120, 150, 180	1	120
2	0	0.8, 0.9, 1, 1.1, 1.2	120
3	30	0.9	80, 120, 160, 200, 240, 280

	Preassigned Displacement	Measured Rotation Angle (°)		Measured Displacement (pixel)		Measured Scaling Factor
Point	Preassigned Displacement	$t = 1$	$t = 2$	$t = 1$	$t = 2$	$t = 1$	$t = 2$
A(120,120)	(−80.47,27.53)	29.53	30.94	(−81,27)	(−81,27)	0.907	0.897
B(−120, −120)	(80.47, −27.53)	29.53	30.94	(80, −28)	(80, −28)	0.907	0.897
C(240, −240)	(55.06,160.94)	30.23	29.53	(55,160)	(55,160)	0.893	0.907
D(−240,240)	(−55.06, −160.94)	30.23	29.53	(−55, −162)	(−55, −162)	0.893	0.907
Maximum RE	−	1.77%	3.13%	1.92%	1.92%	0.78%	0.78%

Scheme	( $u_{0}$ , $v_{0}$ , $θ_{0}$ , $s_{0}$ )	$P_{s e e d}^{0}$	Computation Time	ZNCC
1	(−25, 37, −6.33, 1.37)	--	--	--
2	(−183, 20, −29.88, 1.10)	(−183, −0.0462, 0.5480,20, −0.5480, −0.0462)	73 ms	0.9763
3	(−183, 20, −29.53, 1.10)	(−183, −0.0429, 0.5422,20, −0.5422, −0.0429)	20 ms	0.9763
4	(−183, −20, −30.24, 1.10)	(−183, −0.0497, 0.5540,20, −0.5540, −0.0497)	7 ms	0.9763

Experiments	$θ_{0} (^{\circ})$	$s_{0}$	$N (p i x e l)$
1	0, 30, 60, 90, 120, 150, 180	1	120
2	0	0.8, 0.9, 1, 1.1, 1.2	120
3	30	0.9	80, 120, 160, 200, 240, 280

	Preassigned Displacement	Measured Rotation Angle (°)		Measured Displacement (pixel)		Measured Scaling Factor
Point	Preassigned Displacement	$t = 1$	$t = 2$	$t = 1$	$t = 2$	$t = 1$	$t = 2$
A(120,120)	(−80.47,27.53)	29.53	30.94	(−81,27)	(−81,27)	0.907	0.897
B(−120, −120)	(80.47, −27.53)	29.53	30.94	(80, −28)	(80, −28)	0.907	0.897
C(240, −240)	(55.06,160.94)	30.23	29.53	(55,160)	(55,160)	0.893	0.907
D(−240,240)	(−55.06, −160.94)	30.23	29.53	(−55, −162)	(−55, −162)	0.893	0.907
Maximum RE	−	1.77%	3.13%	1.92%	1.92%	0.78%	0.78%

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Applied Optics