# Super-Resolution Reconstruction of Depth Image Based on Kriging Interpolation
## 2 Depth Image super-resolution Algorithm
### Classical Image Interpolation Methods  
OpenCV2's resize function includes a number of commonly used interpolation algorithms: nearest-neighbour interpolation (INTER_NEAREST) [23], bilinear interpolation (INTER_LINEAR) [24; 25], resampling interpolation (INTER_AREA) [26], cubic interpolation (INTER_CUBIC) [27], and LANCZOS4 cubic interpolation (INTER_LANCZOS4) [28]. Resampling interpolation is based on resampling using the pixel region relationship. Therefore, resampling is preferred in image extraction (decimation). Meanwhile, when the image is zoomed, INTER_NEAREST is preferred. These five classical interpolation algorithms are widely used in industry. However, recent years have seen the emergence of several new interpolation algorithms, including the fractal theory-based algorithm [29], the wavelet algorithm [30], the contour template algorithm [31], the partial differential equation-based algorithm [32], the topography-based inverse distance algorithm [33], and the Kriging algorithm [34]. These algorithms have been shown to have superior performance in various applications, such as image super-resolution, terrain modelling, and geological analysis, and therefore merit consideration for future research.  
This study evaluates the effectiveness of the five classical interpolation algorithms mentioned at the start of the preceding paragraph with respect to the super-resolution of depth images. Using experimental data obtained from the depth image dataset in [35], the depth images and point clouds are first 50% down-sampled and then 200% up-sampled to examine the effectiveness of the interpolation algorithms. The super-resolution results are shown in Figures 1-6 and Table 1, the images show good clarity and completeness after scaling.  
Figure 4: Resampling interpolation (INTER_AREA) results for depth images (PSNR = 33.570 dB). (**a**), depth image; (**b**), front view of the point cloud map of the depth image; (**c**), side view of the point cloud map of the depth image.  
Figure 5: Results of cubic interpolation (INTER_CUBIC) of the depth image (PSNR = 34.515 dB). (**a**), depth image; (**b**), front view of the point cloud map of the depth image; (**c**), side view of the point cloud map of the depth image.  
Figure 3: Bilinear interpolation (INTER_LINEAR) results for depth images (PSNR = 34.164 dB). (**a**), depth image; (**b**), front view of the point cloud map of the depth image; (**c**), side view of the point cloud map of the depth image.  
Figure 6: Lanczos interpolation (INTER_LANZOS24) results for depth images (PSNR = 33.654 dB). (**a**), depth image; (**b**), front view of the point cloud map of the depth image; (**c**), side view of the point cloud map of the depth image.  
The five classical interpolation algorithms are tested experimentally with respect to their ability to meet the requirements of image appearance. In terms of image edge completeness and clarity, the cubic interpolation and Lanczos interpolation algorithms achieve the highest values. However, after conversion of the depth images into point clouds, it is evident that the cubic interpolation and Lanczos interpolation algorithms introduce a large amount of smoothed data to optimise the appearance of the image. From the point cloud or depth distance perspectives, these data can be seen as a source of additional noise. Overall, the above experimental results show that the classical image interpolation algorithms, except the nearest-neighbour interpolation algorithm, inevitably introduce noise that cannot be eliminated. If the images need to be converted to point clouds and reconstructed in 3D, the noise introduced will greatly affect the final result and be difficult to eliminate. If high-quality, super-resolution depth images are to be obtained, improvements are needed, starting with the interpolation algorithm.