## 1 Introduction
However, to obtain the kinematic variables for evaluating the condition of a structure from an image that only provides information on simple shape change or displacement, a process to combine the results (displacement information) with numerical analysis is required. In the past, the method connecting the results to the FEM was mainly used to reproduce the value of a kinematic variable using the displacement information acquired through direct measurement or from an image of any location [16; 17; 18]. [PERSON] et al. [19] improved the computational efficiency and accuracy of the existing digital image correlation technique by combining it with FEM. [PERSON] et al. [20] updated the boundary conditions at the crack tip of a crack propagation in a FEM model by combining the displacement measured by the digital image correlation and FEM. In general, to combine the values measured from digital images using numerical analysis, data are processed by aligning the measurement points of the experiment and the joints of a mesh, or by using the changes in images obtained at certain time intervals. The mesh-dependent FEM possesses the characteristic of interpolation or extrapolation and extracts the strain or stress value at the quadrature point using an element-based approximation function. However, the analysis becomes more difficult in the case of complex target structure shapes or discontinuities such as cracks, because the mesh required for the simulation must be reconfigured at every analysis step. The element-free Galerkin method (EFGM) [21], which does not use a mesh, can avoid the constraints of FEM or the limitation of a mesh. Although the EFGM is a meshless method, its application remains limited because an integration cell similar to a mesh is required for calculating the integral describing the governing equation, which is slightly complicated [22; 23; 24]. In addition, it is necessary to derive the derivative approximation function for calculating kinematic variables;however, the differential calculation for the EFGM approximation function is slightly complex, making it improbable to completely alleviate the difficulties faced in applying the FEM. On the other hand, the strong form-based meshfree method can be used even when the location of the tracking point (TP) that acquires the displacement information through DIP is irregular, because this method simplifies the calculation of the kinematic variables and differentials by using nodes only. Mesh-free-based numerical analysis methods have been studied in various domains to improve the mesh's constraints [25; 26; 27; 28]. The particle difference method (PDM)--a meshfree method that uses a high-speed derivative approximation based on strong form or collocation--makes the computation of displacement, strain, and stress fast and free because of its simple high-dimensional differential computations. Moreover, because this method only uses nodes and not meshes, it does not encounter problems similar to those faced by the FEM during this type of computation, even if the geometric shape used in the analysis varies over time [29; 30; 31; 32]. Furthermore, a method to regenerate stress fields and predict crack occurrence patterns through displacement measurement and meshfree approximation using images has been proposed. However, improving techniques such as the TP extension is challenging, because the applied DIP technique is difficult to scale, and the integration with the meshfree method is still performed by simply adopting the approximation function [3]. However, it is easy to calculate the strain or stress by using the geometric description in the framework of the strong form-based meshfree method. The derivative approximation can be simplified by combining with the DIP technique, thereby quickly and accurately extracting various kinematic variables required for evaluating structural conditions because the strong form-based PDM is \"truly\" a meshfree method.