2.1

Super-resolution model

The super-resolution network, incorporating an attention mechanism [8], comprises three core components: a feature extraction module, an information extraction module, and a reconstruction module. The feature extraction module discerns features from the initial low-resolution image, while the information extraction module dynamically adjusts feature expressiveness using a mapping attention mechanism to enhance the retrieval of finer details like contour textures. Following this, the reconstruction module executes element-wise addition operations on the gathered high-resolution information, facilitating the transformation from low-resolution (LR) input images to high-resolution (HR) output images. The model’s structure is depicted in Figure 2.

Figure 2.

Super-resolution reconstruction model.

The information extraction block used in this paper consists of two 3 × 3 convolutions, both with feature dimensions of 64. The processing involved is described as:

where I_LR represents the input low-resolution image, H_FE denotes the function used for feature extraction, and F₀ represents the extracted features that will be utilized in the subsequent stage of processing. The feature extraction block employs a feature map attention mechanism to prioritize global information, enhancing the model’s focus and feature representation. This integration of local and global features results in more effective and comprehensive feature extraction.

The information extraction block [8] is comprised of three subunits sharing a similar architecture, each employing the feature map attention mechanism. The comprehensive structure of the information extraction unit can be segmented into an information enhancement unit and a compression unit, illustrated in Figure 3. The processing procedure can be described as follows:

Figure 3.

Information extraction block.

where H_i denotes the function that performs the feature extraction, and F_i is both the output of the current information extraction block and the input of the next information extraction block.

The attention module identifies and prioritizes features crucial for the task at hand, enhancing the network’s discriminative ability. In chessboard pattern image calibration, high-frequency corner point information is vital. Therefore, an attention mechanism is introduced to emphasize high-frequency channel details while minimizing redundant information from low-frequency areas, such as edges and textures.

For HR image reconstruction, the module uses features from prior convolutional layers and applies them to the low-resolution image scale. ESPCN [9], known for its efficiency in super-resolution, ensures superior results with faster computation and fewer parameters. It’s ideal for scenarios with limited computational resources. Its network is depicted as:

where HREC and U denote the reconstruction module and the bicubic interpolation operation, respectively, and ISR denotes the final output.

2.2

Corner detection

Corner point detection is required for the super-resolution reconstructed calibration images to achieve high-precision camera calibration. Compared with the Harris corner point detection algorithm, the Shi-Tomasi algorithm [10] shows an improved performance in terms of computational efficiency and stability. In particular, the Shi-Tomasi corner detection algorithm defines a pixel point as a corner point by calculating the response function R = min (λ₁, λ₂), when the value of R is greater than a set threshold. In addition, λ₁ and λ₂ are the eigenvalues of the autocorrelation matrix M with local gray scale variation. Here, M is denoted as:

where w(x, y) is a window function to weigh the gray-scale changes in the local region, ∇I is the gradient vector of the image at pixel point (x,y), and ∇I^T is its transpose.

3.1

Camera calibration experiment

Reprojection error evaluates camera calibration quality; smaller errors indicate closer calibration to real data. Here, the reprojection errors under the two methods were compared by using the calibration methods based on the Harris corner detection approach and on super-resolution corner detection proposed in this paper to calibrate the calibration plate images captured under the same position. Super-resolution increased image resolution from 1624×1234 to 3248×2468 pixels, as depicted in Figure 4. Table 1 compares parameters calculated by both methods.

Figure 4.

Images before and after super-resolution reconstruction. (a) Original image; (b) Super-resolution reconstructed image; (c) Original image corner detection; (d) Corner detection based on super-resolution reconstruction.

Table 1.

Calibration parameters calculated by Harris corner detection and the proposed method.

Referring to the corresponding values of the optimal calibration data, the reprojection errors of the Harris calibration method and the proposed calibration method in this paper can be obtained, as shown in Figure 5.

Figure 5.

The reprojection errors under different calibration methods. (a) Error obtained by the Harris corner detection calibration method and (b) Error obtained from the corner detection calibration method proposed in this article

The calibrated reprojection error obtained under Harris is within 0.15 pixel and the average reprojection error is 0.0561 pixel, and the calibrated reprojection error of the proposed method is within 0.08 pixel and its average reprojection error is 0.1031 pixel. Due to the super-resolution magnification of 2×2, the actual distance corresponding to each pixel point is 0.25 times of the original image. Within the same pixel scale, the reprojection error of the proposed method should be 0.0267 pixel, and its reprojection error is reduced by 47.6%.

3.2

DIC measurement experiment

The experimental setup shown in Figure 6(a) was built to verify the effectiveness of the proposed preprocessing based on super-resolution angular point detection calibration method for DIC testing. The resolution of the camera is 1624×1234 pixels with a 25 mm focal length lens; the calibration plate was a 12 × 9 tessellated grid calibration plate, with the width of a single grid being 6 mm. In this experimental environment, the camera calibration results obtained using different methods in the same camera pose were used to perform geometric reconstruction on the nominal size 60mm standard gauge block shown in Figure 6(b).

Figure 6.

The experimental environment. (a) Experimental setup, (b) 60 mm standard measuring block, and (c) 60 mm standard measuring block for manual spot making.

The search step size was set to 7 pixels, while the search subset size was configured at 21×21 pixels. The geometric reconstruction of the 60 mm standard gauge block in Figure 6(c) was performed using calibration results obtained from the Harris corner detection calibration method and super-resolution corner detection calibration method under the same camera pose. First, one image each was taken with a binocular camera, after which the IC-GN algorithm [11] was used to perform correlation analysis on the two images. Finally, the pixel coordinates were converted into physical coordinates using calibration parameters to calculate the actual measurement results of the standard gauge block.

Figure 7(a) shows the calibration method using Harris corner detection, while Figure 7(b) shows the reconstruction results of the proposed super-resolution corner detection calibration method. The reconstructed size of the gauge block based on the Harris corner detection calibration is 57.9008 mm, whereas the proposed calibration method yields a reconstructed size of 59.0588 mm. This results in a relative error decrease from 3.625% to 1.593%, and a reduction in deviation from 2.0992mm to 0.9412mm. These findings demonstrate that the proposed super-resolution corner detection calibration method enhances the reconstruction accuracy of DIC.

Figure 7.

Geometric reconstruction effect. (a) Measurement results of calibration method based on the Harris comer detection method and (b) Measurement results based on the calibration method proposed in this article.