## 4 Results and Discussion
### DIC-PDDO for Noise Reduction  
In order to analyze the performance of the DIC-PDDO method for strain calculation on the tensile experiment specimen in the case of high gradients, similarly as in [12; 13; 14] (see Figure 1), the minimum DIC VSG size of 33 px (step 1 px) was used for the selected subset size. This DIC calculation setup results in an almost invisible displacement oscillations of 2 \(\upmu\)m magnitude (0.1% of the maximum value) (the oscillations are also called as artificial noise in this study and calculated based on the comparison against the DIC displacement field generated with the DIC step of 7 px used in previous calculations (Figures 7-9) while the effect of real noise from experimental setup is not considered) (Figure 12a) which in turn results in an artificial significant noise of the DIC-calculated \(\varepsilon_{x}\) strains of \(\pm\)0.006 units (33% of the maximum absolute value) (Figure 12b). The strain \(\varepsilon_{x}\) was selected for this evaluation because it is more affected by artificial noise (\(\varepsilon_{y}\) strains are up to 7 times higher than \(\varepsilon_{x}\) strains and thus the noise effect on the \(\varepsilon_{y}\) strains is the same times smaller). The smooth profile of the curve labeled the \"PDDO to noisy DIC\" in Figure 12b shows the ability of the PDDO to eliminate the effect of the oscillatory DIC input displacements on the PDDO calculated strains as opposed to the DIC method of strain calculation which amplifies the slightly oscillatory input in the calculated strains (curve labeled \"DIC noisy\" in Figure 12b). Figure 12: Slight oscillations (artificial noise) introduced in the DIC displacement (**a**), resulting in considerable noise in the DIC strains (**b**). Similar conclusion can be done based on the observation of the PDDO application to synthetic image no. 6 of the plate with hole from DIC Challenge 1.0 Sample 12 (Figure 13, also see Figure 1). While the smaller DIC VSG leads to an oscillatory solution and larger VSG smooths out the strain peaks also reducing the strain spatial resolution, the PDDO solution provides smooth and still accurate strain profile preserving its spatial resolution. The data in Figure 12 represent a snapshot during the specimens deformation, corresponding to 75% of the failure load (DIC image no. 60 in the set of DIC images recorded during deformation). In order to analyze the proposed PDDO method at different levels of deformation, strains were also analyzed at different loading levels of the specimen, from the test start to the specimens failure (DIC image no. 80), and results are plotted in Figure 14. The plots in Figure 14 show increasing absolute differences between the curves with the deformation due to selected artificial noise generation method and the PDDO method is able to eliminate the effects of the input noise at various deformation levels. The DIC method to reduce the noise in the calculated strains is the DIC strain filter (see Figure 3b) which smoothen the calculated strains by averaging over the strain filter area, and reduces thus the noise fluctuations. However, the possibility exists that the real strain peaks and strain gradients are also averaged out by using the DIC strain filter, and the DIC user should carefully select between noisy and smooth but less accurate results [41] (see Section 2.1). The results of our study show that not only the PDDO method provides a smoother (less oscillatory) strain solution (Figures 10-14), but it also preserves the accuracy of the results, as shown in Figure 15. Here the same strain field results, namely the \"noisy DIC\" generated by using a DIC step size of 1 px (Figure 15a), the \"PDDO to noisy DIC\" generated by applying the PDDO to the slight oscillatory input displacements from the \"noisy DIC\" setup (Figure 15b), and the \"not noisy DIC\" generated by using a DIC step size of 7 px (Figure 15c), are analyzed. Figure 13: The problem of plate with hole analyzed in [12; 13; 14] (also see Figure 1) extended by the DIC-PDDO strain solution.