# Super-Resolution Reconstruction of Depth Image Based on Kriging Interpolation
## 1 Introduction  
With the development of computer vision and image processing, deep image processing has become a hot research topic in recent years. Deep image processing has both theoretical significance and important practical applications. For example, in the field of virtual reality video games, where the player's pose movements are acquired through somatosensory devices and subjected to human-computer interaction and modelling, depth images acquired in real time must be processed to improve the quality of the models constructed from depth data. Another topic of importance is the super-resolution reconstruction of depth images, which is critical for applications in vision fields such as virtual reality video games, biomedicine, and augmented reality, as these applications require highly accurate depth image data. High-precision super-resolution reconstruction helps generate highly realistic three-dimensional (3D) object surface models. In addition, artificial intelligence and autonomous driving both require highly accurate depth image data. Developments in computer vision and image processing promise to make the exploration of depth-image-based super-resolution algorithms a research hotspot. Recently, image super-resolution using deep learning methods has achieved remarkable success in producing high-quality and visually pleasing results [1; 2; 3]. However, these methods usually require a large amount of training data and computational resources, making them impractical for real-time applications. To overcome this limitation, some researchers have explored the use of non-deep learning-based techniques, such as interpolation-based methods [4; 5]. While these methods are computationally efficient, they may not be suitable for processing complex depth images. Recently, a few studies have proposed the use of fractional-order differentiation in interpolation-based methods for depth image super-resolution [6; 7]. These methods have been shown to be effective in preserving texture information and edge features as well as improving noise reduction performance. In comparison with traditional interpolation-based methods, these methods offer better image reconstruction and greater robustness. Depth image super-resolution is a signal processing technique for obtaining high-resolution images from single or multiple frames of low-resolution images [8] and has promising practical applications [9]. Image super-resolution techniques can be broadly classified into four categories: interpolation-based [10], reconstruction-based [11], enhancement-based [12], and learning-based [1; 2] methods. Fractional-order calculus has been widely applied in cybernetics, probability theory, and signal processing [13]. One study [14] proposed a numerical implementation of fractional-order calculus in the field of signal analysis and its initial application to two-dimensional (2D) image processing; the same study also proposed the Tiansi mask operator based on fractional-order calculus, which achieved good results in the field of image enhancement and edge detection. Other studies [15; 16; 17] have proposed image denoising algorithms based on a small probability model and gradient-adaptive fractional-order calculus, achieving good results in image denoising and enhancement. Spatial interpolation is a technique used to obtain attribute information at the unsampled points (interpolation points) by studying the attribute information of the sampled points. Using a mathematical model, the mapping relationship between the attribute domain and the spatial domain is analysed on the basis of known information from a certain number of sampled points [18]. Spatial interpolation techniques are widely used in tasks such as precipitation prediction, soil level classification, and groundwater simulation [19].