# Super-Resolution Reconstruction of Depth Image Based on Kriging Interpolation
## 4 Kriging Interpolation Super-Resolution Algorithm Based on Fractional-Order Differentiation  
Depth images consist of ordered distance data distributed spatially, and the orderliness makes them conducive to parallel computation, a technology that may realise efficient filtering and convolution computation in the future. Depth images also contain peripheral correlation, and the high-frequency points of edges can be identified by fractional-order differentiation. The high-frequency points are interpolated using the spatial local neighbourhood, while the non-high-frequency points are interpolated by Kriging interpolation. The flowchart in Figure 10 depicts the fractional-order differential Kriging interpolation super-resolution model, which is divided into the following processes: acquiring the depth image, down-sampling the depth image, performing fractional-order differential edge detection, interpolating the down-sampled depth map using the fractional-order differential Kriging interpolation super-resolution model, and obtaining the high-resolution depth image. Table 2 shows the comparison between the kriging interpolation algorithm based on fractional order differentiation and the nearest neighbor interpolation algorithm. It can be seen that the PSNR of kriging interpolation based on fractional order differentiation is better than the nearest neighbor interpolation algorithm. Using open-source datasets [35], a comparison of nearest-neighbour interpolation and Kriging interpolation is performed. In the Kriging interpolation method, the images are first up-sampled by 200% and then down-sampled by 50%. As shown in Table 2, using peak signal-to-noise ratio (PSNR) as the evaluation metric, Kriging interpolation outperforms nearest-neighbour interpolation in terms of reflecting texture details. Specifically, the super-resolution method based on fractional-order differential Kriging interpolation improves the PSNR by 3-18 dB, a significant enhancement. The super-resolved depth images are converted into point cloud maps for comparative analysis, and it can be seen that most of the edges are correctly recovered. These experimental results show that the fractional-order differential Kriging interpolation algorithm performs very well in the super-resolution of depth images and has significance for further research and application. Figure 10: Super-resolution flow chart. The super-resolution results are shown in Figure 11 and Table 2, it can be seen that the edge blurring problem can be solved by edge detection, but the adoption of the simple nearest-neighbour interpolation scheme also causes unwanted jagged edge effects. Subsequently, the super-resolution model based on Kriging interpolation is verified for larger-scale magnification factors using 25% down-sampling and 400% up-sampling. The data in Table 3 show that the super-resolution method based on Kriging interpolation via fractional-order differential edge detection achieves a greater improvement in super-resolution than that of nearest-neighbour interpolation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Datasets [35] Number**} & \multicolumn{2}{c}{**Fractional-Order Differential Kriging**} & \multicolumn{2}{c}{**Nearest**} \\  & \multicolumn{2}{c}{**Interpolation**} & \multicolumn{2}{c}{**Neighbor Interpolation**} \\ \cline{2-4}  & \(\mathbf{v}\) & **PSNR** & **PSNR** \\ \hline
00033 & 0.6 & 33.457 & 29.795 \\ \hline
03236 & 0.6 & 37.230 & 27.738 \\ \hline
03528 & 0.6 & 38.598 & 29.868 \\ \hline
04797 & 0.6 & 47.182 & 26.580 \\ \hline
05989 & 0.6 & 39.888 & 29.468 \\ \hline
08343 & 0.6 & 38.391 & 25.008 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fractional-order differential Kriging interpolation super-resolution (200%). Figure 11: Validation of fractional-order differential Kriging interpolation super-resolution model (dataset no. 00333).