## 2 Digital Image Processing for Tracking Target Point Displacement
### Displacement Tracking of the Tracking Point (TP) Using DIP  
The images acquired using a digital camera contained a set of pixels composed of a color model; in this study, an RGB color model was used. The color model expressed an object through a combination of three-color channels, with each channel having a total color intensity of 256 levels from 0 to 255. Although the use of the RGB color model presents the advantage of expressing \(256\times 256\times 256=16,777,216\) colors, it is inefficient from the perspective of data analysis because it is high-dimensional and requires a large amount of computation. For effective image analysis, it is common to reduce the data size by transforming a three-dimensional (3D) color image obtained by a DSLR camera into a two-dimensional (2D) grayscale image or a binary image expressed. In this study, to reduce the data size, only the remaining ROI target area, which was generated in the pre-process after removing the parts other than the value similar to the color intensity inside the target, was transformed into a binary image (Figure 4). In this process, the second data-reduction process is initiated, and the pixel size constituting the target area is 21,870 \(\times\) 2 = 43,740, which removes 99% of the original image and 99% of the ROI image, thus greatly improving the DIP calculation efficiency. The pixels of the initially acquired image contain irregular noise because of the influence of illumination or light dispersion. This noise interferes with the image analysis. To remove this noise, the erosion operation of morphological image processing, which reduces the image size by removing the outer pixels of the pixel set, was applied. This operation corrects the image by sequentially comparing the structuring element (SE) composed of a \(3\times 3\) matrix with the target image, and selecting the pixel containing all nine elements of SE. The erosion operation can be expressed as follows:  
\[Erosion:E(I,S)\ =\ \underset{s\in S}{\cap}(I+s), \tag{3}\]  
where \(I\) represents the image to which the erosion operation is applied; \(S\) denotes the set of pixels in which the structuring elements applied to the entire image are combined; and \(s\) denotes the structuring element composed of a \(3\times 3\) matrix. Later, the strain and stress caused by the loading of the specimen are calculated by applying the displacement of the TP obtained through DIP in the framework of the PDM. The larger the number of TP displacements, the higher the calculation accuracy. In this study, two target tracking methods were proposed to compare their accuracies based on the number of TPs provided by the combination of DIP and PDM. Figure 5a shows the method of tracking only one point of the centroid of the target (Case 1), and Figure 5b illustrates the method of tracking both line segments connecting the centroid of the target to the centroid of the surrounding target and the point where the boundary of the original target intersects (Case 2). In Case 2, the number of intersection points generated according to the arrangement of the surrounding targets was 3, 5, and 8. Figure 4: Target extraction procedure from ROI. In this study, a rectangular target that exhibited similar behavior as the specimen object, with which it was easier to perform additional analyses using vertices than other types, and that could perform the effect analysis of the rotation, was used. Rectangle targets change with the deformation of the part and have vertices, which are excellent for easily increasing the tracking points. In addition, the centroid of the pixels constituting the target was named the TP, and the intersection points of the line that connects this TP with the centroid of the neighboring target and the outline of the target were named as the expanded tracking point (ETP). Consequently, Case 1 only tracks one TP, whereas Case 2 tracks both the TP and the ETP.