Digital Image Correlation Measurement Based on Pointwise Moving Least-Square Fitting

Fig. 2. Principle of pointwise moving least square method. (a) Schematic of support domain; (b) a fitting window; (c) schematic of local displacement field

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Fig. 3. Crack treatment method. (a) Crack does not penetrate the window; (b) crack runs through the window

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Fig. 4. DIC displacement fields in the reference image and region of interest. (a) Reference image; (b) displacement field $u_{1}$ ; (c) displacement field $u_{2}$ ; (d) displacement field $u_{3}$

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Fig. 5. Root mean square errors of the two methods under three kinds of deformation. (a) Displacement field; (b) strain field

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Fig. 6. Fitting results of displacement field and strain field under the mean value of same $y$ coordinate. (a) Displacement field; (b) strain field

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Fig. 7. Target image and fitting results of discontinuous displacement field. (a) Target image; (b) fitting results

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Fig. 8. sample15 test. (a) Reference image; (b) target image; (c) displacement field obtained by DIC

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Fig. 9. Fitting results for strain field. (a) PLS-1; (b) PMLS-1; (c) PLS-3; (d) PMLS-3

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Fig. 10. Comparison of strain field results at thin lines

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Fig. 11. Fitting results of vertical strain field and local enlargements. (a) PLS-1; (b) PMLS-1; (c) PLS-3; (d) PMLS-3

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Fig. 12. Comparison of vertical strain field results at thin lines

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Table 1. Optimal window size and root mean square error of the two methods under different deformations

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Table 1. Optimal window size and root mean square error of the two methods under different deformations

Deformation	Item		PLS-1	PLS-2	PLS-3	PMLS-1	PMLS-2	PMLS-3
$u_{1}$	Displacement	Window size	5	5	5	5	5	5
	Displacement	$E_{R M S}$ /pixel	0.155	0.107	0.107	0.133	0.107	0.107
	Strain	Window size	5	5	9	5	5	11
	Strain	$E_{R M S}$ /10^-3	3.535	3.400	2.793	3.360	3.268	2.815
$u_{2}$	Displacement	Window size	5	5	5	5	5	5
	Displacement	$E_{R M S}$ /pixel	0.091	0.064	0.064	0.079	0.064	0.064
	Strain	Window size	5	5	11	5	5	13
	Strain	$E_{R M S}$ /10^-3	1.520	1.484	1.211	1.456	1.436	1.218
$u_{3}$	Displacement	Window size	5	7	7	5	9	9
	Displacement	$E_{R M S}$ /pixel	0.044	0.032	0.032	0.039	0.032	0.032
	Strain	Window size	5	5	15	5	5	21
	Strain	$E_{R M S}$ /10^-3	0.542	0.547	0.447	0.540	0.547	0.450

Table 2. Calculation time of the three methods

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Table 2. Calculation time of the three methods

Method	Window size is 5	Window size is 9	Window size is 13	Window size is 17	Window size is 21	Window size is 25	Window size is 29
PLS-1	1.528	1.781	2.291	3.003	3.594	4.139	4.535
PMLS-1	2.002	2.659	3.708	5.027	6.671	8.603	10.890
MLS-1	251.797	260.140	267.576	272.980	281.033	287.159	293.716

Table 3. Conditional numbers of matrix $A$

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Table 3. Conditional numbers of matrix $A$

Method	Support domain is 5	Support domain is 9	Support domain is 13	Support domain is 17	Support domain is 21	Support domain is 25	Support domain is 29
MLS-1	8.687×10⁸	3.375×10⁸	1.766×10⁸	1.075×10⁸	7.175×10⁷	5.094×10⁷	3.781×10⁷
PMLS-1	4	10	18.667	30	44	60.667	80
MLS-2	5.760×10¹⁷	7.267×10¹⁶	1.922×10¹⁶	7.011×10¹⁵	3.095×10¹⁵	1.551×10¹⁵	8.509×10¹⁴
PMLS-2	13.356	76.890	2.860×10²	7.760×10²	1.728×10³	3.367×10³	5.966×10³
MLS-3	2.155×10²³	1.450×10¹⁶	4.400×10¹⁶	9.144×10¹⁶	1.678×10¹⁷	2.177×10¹⁷	1.650×10¹⁷
PMLS-3	53.201	5.833×10²	4.271×10⁴	1.913×10⁴	6.374×10⁴	1.735×10⁵	4.093×10⁵

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Shuang Fan, Yurong Guo. Digital Image Correlation Measurement Based on Pointwise Moving Least-Square Fitting[J]. Laser & Optoelectronics Progress, 2023, 60(6): 0612001

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