In recent years, high elongation materials are widely used. Therefore, it is important to investigate the tensile properties of high elongation materials for engineering applications. Video extensometer is equipment for measuring the materials’ tensile properties. It uses image processing technology to match data points and measures the actual deformation. However, when measuring high elongation materials, motion blur will appear on the collected images, which can affect the accuracy of image matching. In this paper, we proposed an image matching method which is based on Local Phase Quantization (LPQ) features to reduce the interference of the motion blur and improve the accuracy of the image matching algorithms as well. The experimental results on simulations show that the proposed initialization method is sufficiently accurate to enable the correct convergence of the subsequent optimization in the presence of motion blur. The experiment of uniaxial tensile also verifies the accuracy and robustness of the method.
High elongation materials are an important class of materials for structural applications such as transportation, civil infrastructures, and biomedical applications. In actual service conditions, these materials are often subject to both mechanical and environmental loads. These factors will change the material properties and thus have a great influence on the service life and safety performance of these materials. In order to study these factors, the tensile mechanical test should be carried out on these materials.
At present, the most commonly used equipment for the tensile mechanical test is the mechanical extensometer and video extensometer. For the high elongation materials, the mechanical extensometer which is mounted directly onto the material via blade causes many problems such as the following: (1) mutual friction will reduce the measurement accuracy; (2) the total deformation cannot be easily measured in the uniaxial tensile test; (3) the measuring range is limited. Compared with mechanical extensometer, the video extensometer has the following advantages over mechanical extensometer: (1) it has no abrasion on the material; (2) it is applied for different types of specimen and material properties; (3) its measuring range is not limited; (4) it has high precision [
Compared with mechanical extensometer, video extensometer has obvious advantages in engineering applications. However, if higher accuracy is pursued, some influence factors can not be ignored, such as out-of-plane displacement, self-heating of the camera, lens distortion, and image blur induced by motion. Reference [
Despite these advances, few works about eliminating extensometer’s measurement errors caused by motion-induced image blur to improve the accuracy have been reported. In this paper, we will propose an image matching method for video extensometer to measure the parameters by utilizing Local Phase Quantization (LPQ) feature. This method is robust and performs well on images with serious motion blur and deformation.
The rest of the paper is organized as follows. The basic principle of video extensometer is described in Section
A schematic diagram of the video extensometer system is shown in Figure
Measurement system overview.
For measurement, first, make the spackle pattern on the material surface, keep the CCD camera’s optical axis vertical to the test specimen surface, choose the appropriate focal length, and make sure the field of view covers the whole material. In the tensile stress test, the position of the data point will be changed before and after the deformation. Through the deformation images collected by CCD camera at different times, we can calculate the materials’ tensile properties.
The video extensometer uses DIC to analyze materials tensile properties [
Procedures of DIC.
As shown in Figure
For the shape function
The corresponding matrix form is
Images are obtained in discrete form and intensity values are recorded as “pixels.” But the integer pixel locations do not satisfy the accuracy of extensometer. In order to improve the precision of video extensometer, we use subpixel displacement measurement algorithm to get the subpixel displacement. The correlation coefficient curve fitting method, iterative algorithm, and gradient-based algorithm are the three most common methods [
The displacement refined by optimizing correlation using N-R iteration algorithm needs to calculate the correlation coefficient which describes the similarity between the reference subset and the target subset. In the actual situation, the spackle pattern will be affected by the lighting condition and the deformation. Tong [
Finally, use the optimal parameter which minimizes ZNSSD to calculate the data point displacement and get the materials tensile properties.
When the CCD camera collects an image, the image may represent the scene over a period of time, known as the exposure time. But the relative motion between the camera and material during exposure time may result in a blurring image which is motion blur.
The ideal lens imaging model is shown in Figure
Ideal lens imaging model.
Based on the tension speed
Using (
The blur distance for various types of lenses and tensile rate.
Focal length (mm) | Image distance (mm) | Size of pixel ( | Exposure time (s) | Tensile rate (mm/min) | Object distance (mm) | Blur distance ( | Blur pixel (pix) |
---|---|---|---|---|---|---|---|
20 | 21.42 | 5.2 | 0.01 | 100 | 300 | 1.19 | 0.23 |
50 | 60 | 5.2 | 0.01 | 100 | 300 | 3.33 | 0.64 |
80 | 109.09 | 5.2 | 0.01 | 100 | 300 | 6.06 | 1.17 |
20 | 21.42 | 5.2 | 0.01 | 200 | 300 | 2.38 | 0.46 |
50 | 60 | 5.2 | 0.01 | 200 | 300 | 6.67 | 1.28 |
80 | 109.09 | 5.2 | 0.01 | 200 | 300 | 12.12 | 2.33 |
20 | 21.42 | 5.2 | 0.01 | 500 | 300 | 5.95 | 1.14 |
50 | 60 | 5.2 | 0.01 | 500 | 300 | 16.66 | 3.21 |
80 | 109.09 | 5.2 | 0.01 | 500 | 300 | 30.30 | 5.83 |
As we can see from Table
Rubber tensile images.
In order to get more accurately measured result, we use N-R iteration algorithm, but the convergent range of N-R iteration algorithm is only a few pixels [
The conventional method for initializing the deformation parameter is using integer pixel displacement search. It is used to find the peak position of the correlation coefficient in a deformed image pixel by pixel. However, this method depends on gray information; it cannot handle large rotation and motion blur, because it assumes the subset shape is unchanged [
It can be seen that image blur will change the image information and make it difficult to identify the data point, thus affecting the video extensometer measurement accuracy. In order to make the video extensometer more accurate, we need to eliminate the influence of motion blur on integer pixel displacement search. For blurred images matching, conventional methods are based on a prior knowledge of the blurred image to restore a clear image [
Based on the above ideas, this chapter proposes an integer pixel searching algorithm based on LPQ feature [
In digital image processing, the discrete model for spatially shift-invariant blurring of an ideal image
The LPQ feature model is based on the following assumptions: (1) the noise pollution can be ignored; (2) the PSF is the centrally symmetric. Depending on the above assumption, (
In the Fourier domain, this corresponds to
Because the PSF
From the above equation, when
The LPQ feature is based on the blur invariance property of the Fourier phase spectrum described in Section
In LPQ, only four frequency points are considered, such as
The phase information in the Fourier coefficients is recorded by examining the signs of the real and imaginary parts of each component in
Finally, a histogram is formed by all the positions in the rectangular region and used as a 256-dimensional feature vector in the match.
In this section, we introduce the key procedure of the matching algorithm. First, input a series of images, select the first one as the un-deformed image, and then select a data point
Flowchart for the algorithms routine: (a) undeformed image, (b) deformed image, (c) LPQ descriptor of reference subset, (d) LPQ descriptor of target subset, and (e) Chi-Square value.
According to Chi-Square statistics, the location of the minimum value of
In order to assess the performance of the initialization using LPQ matching, we performed uniaxial tensile experiments. In the DIC calculation, deformed images are generated by the bicubic spline interpolation. ZNSSD is selected as the objective function. The optimization is terminated if the change of ZNSSD is less than
The simulated images are assumed to be the sum of individual Gaussian speckles:
Simulate spackle pattern. (a) undeformed image; (b) the data point in the undeformed image.
In this experiment, a series of deformed images are generated using the bicubic spline interpolation method with a range of 0.1–0.9 pixels by step of 0.1 pixels between successive images. We use the first image as the undeformed image, as shown in Figure
Results of the conventional method.
Exact value | Mean error | Maximum error | Standard deviation |
---|---|---|---|
0.3 | 0.005421 | 0.007142 | 0.006942 |
0.6 | 0.004254 | 0.016541 | 0.005987 |
0.9 | 0.004852 | 0.023214 | 0.008532 |
1.2 | 0.004024 | 0.019654 | 0.008974 |
1.5 | 0.006104 | 0.012100 | 0.012746 |
1.8 | 0.005845 | 0.008451 | 0.010924 |
2.1 | 0.005112 | 0.013542 | 0.010572 |
2.4 | 0.007521 | 0.016587 | 0.011348 |
2.7 | 0.007310 | 0.018547 | 0.012679 |
Unit:
Results of proposed method.
Exact value | Mean error | Maximum error | Standard deviation |
---|---|---|---|
0.3 | 0.002977 | 0.004726 | 0.005061 |
0.6 | 0.001535 | 0.003642 | 0.005682 |
0.9 | 0.001735 | 0.003623 | 0.007752 |
1.2 | 0.001606 | 0.003372 | 0.008871 |
1.5 | 0.001683 | 0.002956 | 0.010356 |
1.8 | 0.002745 | 0.004856 | 0.010449 |
2.1 | 0.003995 | 0.006735 | 0.008532 |
2.4 | 0.002234 | 0.004235 | 0.007263 |
2.7 | 0.003962 | 0.005275 | 0.005625 |
Unit:
To further illustrate the advantage of using LPQ feature in the initialization of DIC, we add the motion blur on the spackle pattern range from 0 to 10 pixels and step by 2 pixels. Considering when the materials fracture, the extension rate will increase rapidly and add the maximum fuzzy scale to 10 pixels as well. The proposed method is compared with the conventional method in the blurred spackle pattern. The mean error and the standard deviation of the two different methods on different motion blur are shown in Figures
Comparison of mean error between the two search methods.
Comparison of standard deviation between the two search methods.
It can be analyzed that, with the increase of the motion blur, the mean error and the standard deviation of the conventional method increase; however, the accuracy of the proposed method is steady because of LPQ feature, but the conventional method cannot search the integral pixel displacement accurately when motion blur changes the image gray information.
The size of reference subset is an important parameter in DIC. When the size of subset region is smaller, computational efficiency is higher. However, less information contained in the smaller subset may reduce the match accuracy. If we increase the subset size, it can reduce the noise impact and get more accurate results. However, the calculation will increase proportionally with the subset size increase.
We choose reference subset size from 11 × 11–71 × 71 pixels and then increase it by
Comparison of standard deviation between different subset regions.
In the presented video extensometer system, images are captured with
The shape of the high elongation specimen typically used for uniaxial tensile tests follows the GB/T 528-2009 standard. The width of the specimen is
During the experiment, we use the first image as the undeformed image and other 5 images at different times as the deformed images. On the undeformed image, we choose 50 data points on the same line and calculate its displacement. The average displacement and average ZNSSD values for these data points at different deformed images are listed in Table
Results of proposed method.
Number | Average displacement | |
---|---|---|
1 | 225.00, 90.26 | 0.0092 |
2 | 225.00, 89.22 | 0.0218 |
3 | 225.12, 85.36 | 0.0081 |
4 | 225.56, 71.51 | 0.0116 |
5 | 225.48, 19.55 | 0.0209 |
Results of the conventional method.
Number | Average displacement | |
---|---|---|
1 | 225.00, 90.86 | 0.0160 |
2 | 225.00, 89.04 | 0.0320 |
3 | 225.20, 84.52 | 0.0360 |
4 | 225.96, 70.98 | 0.0680 |
5 | 225.58, 18.34 | 0.0940 |
In Table
In this paper, we propose a novel integer pixel searching algorithm based on LPQ feature utilized in the video extensometer system that can match the data points during the uniaxial tensile testing.
Experimental results on simulated speckle images verify that this algorithm is better than conventional methods, the maximum mean error is only 0.003995
In conclusion, the algorithm can bring a more accurate and more intelligent measurement technique for measuring full-field displacements of high elongation materials.
The authors declare that they have no competing interests.
The authors would like to thank Xiaofang Yuan for his constructive suggestions. This work is supported by the National Natural Science Foundation of China (Grant no. 61501181), by the National Science and Technology Major Project of China (Grant no. 07-Y30B10-9001-14/16), by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and by Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology.