# Super-Resolution Reconstruction of Depth Image Based on Kriging Interpolation
## 4 Kriging Interpolation Super-Resolution Algorithm Based on Fractional-Order Differentiation
(**a**,**d**,**g**) Original depth images; (**b**,**e**,**h**) Outputs of fractional-order differential Kriging interpolation super-resolution model (\(\
u=0.6\), PSNR \(=33.299\) dB); (**c**,**f**,**i**) Outputs of nearest-neighbour interpolation super-resolution model (PSNR \(=29.795\) dB). The super-resolution results are shown in Figures 12-18 and Table 3. The results of Figure 12 are compared in side view in Figure 13 as an example. As can be seen from Figure 13, the results of the interpolation methods differ in the details. The edge detection method using fractional-order differentiation is implemented to solve the problem of blurred edge points. In terms of texture details, the Kriging interpolation yields more details than the nearest-neighbour interpolation. In particular, the Kriging interpolation yields results with more texture details and a certain level of randomness and fractal characteristics, indicating its superiority over inverse distance interpolation in terms of detail representation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Datasets [35]** & \multicolumn{2}{c}{**Fractional-Order Differential Kriging Interpolation**} & \multicolumn{2}{c}{**Nearest-Neighbour Interpolation**} \\ \cline{2-4}
**Number** & \(\mathbf{v}\) & **PSNR** & **PSNR** \\ \hline
00033 & 0.6 & 28.828 & 25.385 \\ \hline
03236 & 0.6 & 32.290 & 23.383 \\ \hline
03528 & 0.6 & 33.677 & 25.825 \\ \hline
04797 & 0.6 & 40.595 & 22.456 \\ \hline
05989 & 0.6 & 34.459 & 25.503 \\ \hline
08343 & 0.6 & 33.819 & 21.051 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Super-resolution results of the method based on fractional-order differential Kriging interpolation (400% up-sampling) and the nearest-neighbour interpolation method. Figure 12: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 00333). (**a**,**d**,**g**) Original depth images; (**b**,**e**,**h**) Outputs of fractional-order differential Kriging interpolation super-resolution model (\(v=0.6\), PSNR \(=28.828\) dB); (**c**,**f**,**i**) Outputs of nearest-neighbour interpolation super-resolution model (PSNR \(=25.385\) dB). Figure 14: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 05989). (**a**,**d**,**g**) Original depth images; (**b**,**e**,**h**) Outputs of fractional-order differential Kriging interpolation super-resolution model (\(\
u=0.6\), PSNR = 34.459 dB); (**c**,**f**,**i**) Outputs of nearest-neighbour interpolation super-resolution model (PSNR = 25.503 dB). Figure 13: Comparison of details of the Kriging and nearest-neighbour interpolation algorithms. Figure 16: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 03528). (**a,d,g**) Original depth images; (**b,e,h**) Outputs of fractional-order differential Kriging interpolation super-resolution model (\(\
u\) = 0.6, PSNR = 33.677 dB); (**c,f,i**) Outputs of nearest-neighbour interpolation super-resolution model (PSNR = 25.825 dB). Figure 15: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 03236). (**a,d,g**) Original depth images; (**b,e,h**) Outputs of fractional-order differential Kriging interpolation super-resolution model (\(\
u\) = 0.6, PSNR = 32.290 dB); (**c,f,i**) Outputs of nearest-neighbour interpolation super-resolution model (PSNR = 23.383 dB). Figure 17: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 04797). (**a,d,g**) Original depth images; (**b,e,h**) Outputs of fractional-order differential Kriging interpolation super-resolution model (\(\
u=0.6\), PSNR = 40.595 dB); (**c,f,i**) Outputs of nearest-neighbour interpolation super-resolution model (PSNR = 22.456 dB). Figure 18: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 04797).