# Digital Image Correlation with a Prism Camera and Its Application in Complex Deformation Measurement

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## Abstract

**:**

## 1. Introduction

## 2. Algorithm

#### 2.1. Principle

#### 2.2. Integer-Pixel Matching

#### 2.3. Sub-Pixels Matching

#### 2.4. Initial Value Estimation of Light Intensity Coefficients

## 3. Numerical Simulation

#### 3.1. Generate Speckle Image

_{k}is the position and strength of the k-th speckled particle. $({x}_{k}^{\prime},{y}_{k}^{\prime})$ is the position of the k-th speckle particle after translation. It is described by displacement function before and after translation:

^{2}, the particle size is 4 pixels, and the particle number is 7000. On the reference image of each channel, a displacement function with a period T of 20 and amplitude $\alpha $ of 0.5 pixels is applied first. Then, add the light intensity transformation with (a, b) of (0.95, 8), (0.93, 12), and (0.94, 10) on the three channels, respectively. Finally, color speckle images before and after deformation are synthesized. The color reference image is shown in Figure 5a. To compare with the traditional method, the gray speckle image is obtained by graying the color image before and after deformation. The weighted average factor used for graying is (0.299, 0.578, 0.114). The grayscale reference image is shown in Figure 5b. An improved algorithm (called color FA-GN) is used on color speckle images, and a traditional algorithm (called gray FA-GN) is used on gray speckle images. Both choose bilinear interpolation and first-order shape function. To ensure that the amount of information involved in matching the subset is basically the same in the two algorithms, seven groups of different subset sizes in Table 1 are selected for comparative calculation. Using the Intel Core i7 processor, run the computer with 16G memory to execute the written program.

^{2}.

#### 3.2. Result Analysis

## 4. Application

^{−2}mm/pixel.

^{2}and the step length is 10 pixels. Due to space limitations, four compression states are chosen in Figure 11a. The calculated deformation field in horizontal and vertical directions are shown in Figure 11b–e, respectively. The maximum and minimum displacements in the horizontal and vertical directions in each state are shown in the lower right corner of each figure. It can be clearly seen that the measurement results are smooth, and the distribution trend is correct. This reflects the value of the color image-matching algorithm in practical applications.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### IC-GN Matching Algorithm Based on Color Image

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Group Number | Subset Size | U-Field Displacement Deviation Statistics (×10^{−3}) | V-Field Displacement Deviation Statistics (×10 ^{−3}) | Average Value of Iterations | |||
---|---|---|---|---|---|---|---|

MAE | RMSE | MAE | RMSE | Time (×10^{−4} s) | Times | ||

(1) | (2 × 9 + 1)^{2} | 6.60 | 8.16 | 6.98 | 8.77 | 5.60 | 4.92 |

(2 × 5 + 1)^{2} × 3 | 8.94 | 11.12 | 8.17 | 10.49 | 9.25 | 5.66 | |

(2) | (2 × 11 + 1)^{2} | 6.42 | 8.37 | 6.57 | 8.64 | 6.51 | 4.78 |

(2 × 6 + 1)^{2} × 3 | 7.70 | 9.53 | 6.99 | 8.66 | 9.57 | 5.39 | |

(3) | (2 × 13 + 1)^{2} | 8.10 | 10.96 | 7.54 | 10.32 | 7.81 | 4.68 |

(2 × 7 + 1)^{2} × 3 | 6.70 | 8.32 | 6.14 | 7.64 | 10.85 | 5.25 | |

(4) | (2 × 15 + 1)^{2} | 11.28 | 15.23 | 10.40 | 14.06 | 9.36 | 4.68 |

(2 × 8 + 1)^{2} × 3 | 5.86 | 7.29 | 5.64 | 7.09 | 13.83 | 5.12 | |

(5) | (2 × 16 + 1)^{2} | 13.17 | 17.59 | 12.02 | 16.14 | 10.21 | 4.70 |

(2 × 9 + 1)^{2} × 3 | 5.52 | 6.87 | 5.22 | 6.69 | 15.17 | 5.02 | |

(6) | (2 × 18 + 1)^{2} | 17.59 | 22.90 | 15.65 | 20.59 | 11.58 | 4.64 |

(2 × 10 + 1)^{2} × 3 | 5.42 | 6.95 | 4.94 | 6.60 | 17.06 | 4.98 | |

(7) | (2 × 20 + 1)^{2} | 22.80 | 28.84 | 20.19 | 26.18 | 13.90 | 4.62 |

(2 × 11 + 1)^{2} × 3 | 5.70 | 7.63 | 5.19 | 7.18 | 18.57 | 4.94 |

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**MDPI and ACS Style**

Hu, H.; Qian, B.; Zhang, Y.; Li, W.
Digital Image Correlation with a Prism Camera and Its Application in Complex Deformation Measurement. *Sensors* **2023**, *23*, 5531.
https://doi.org/10.3390/s23125531

**AMA Style**

Hu H, Qian B, Zhang Y, Li W.
Digital Image Correlation with a Prism Camera and Its Application in Complex Deformation Measurement. *Sensors*. 2023; 23(12):5531.
https://doi.org/10.3390/s23125531

**Chicago/Turabian Style**

Hu, Hao, Boxing Qian, Yongqing Zhang, and Wenpan Li.
2023. "Digital Image Correlation with a Prism Camera and Its Application in Complex Deformation Measurement" *Sensors* 23, no. 12: 5531.
https://doi.org/10.3390/s23125531