Depth image enhancement techniques can help to improve image quality and facilitate computer vision tasks. Traditional image-enhancement methods, which are typically based on integer-order calculus, cannot exploit the textural information of an image, and their enhancement effect is limited. To solve this problem, fractional differentiation has been introduced as an innovative image-processing tool. It enables the flexible use of local and non-local information by taking into account the continuous changes between orders, thereby improving the enhancement effect. In this study, a fractional differential is applied in depth image enhancement and used to establish a novel algorithm, named the fractional differential-inverse-distance-weighted depth image enhancement method. Experiments are performed to verify the effectiveness and universality of the algorithm, revealing that it can effectively solve edge and hole interference and significantly enhance textural details. The effects of the order of fractional differentiation and number of iterations on the enhancement performance are examined, and the optimal parameters are obtained. The process data of depth image enhancement associated with the optimal number of iterations and fractional order are expected to facilitate depth image enhancement in actual scenarios.

The super-resolution of depth images is a research hotspot. In this study, the classical Kriging algorithm is applied to the spatial interpolation of depth images, together with the fractional-order differential method for edge recognition, to realise the super-resolution reconstruction of depth images. The resulting interpolation model improves the edge performance of Kriging interpolation by harnessing the superior characteristics of fractional-order differential edge recognition and effectively solving the edge blurring problem in super-resolution interpolation of depth images. Experimental results show that, compared with the classical algorithms, the super-resolution reconstruction based on Kriging interpolation is greatly improved in terms of visual effects and the peak signal-to-noise ratio of the depth image. In particular, edge recognition based on fractional-order differentiation solves the image blurring problem at the edges of the depth images. Inspection of the point clouds of the depth images shows that the output of the proposed interpolation model has obvious fractal characteristics.

High-quality image restoration is typically challenging due to low signal–to–background ratios (SBRs) and limited statistics frames. To address these challenges, this paper devised a method based on fractional-order total variation (FOTV) regularization for recovering Geiger-mode avalanche photodiode (GM-APD) light detection and ranging (lidar) depth images. First, the spatial differential peak-picking method was used to extract the target depth image from low SBR and limited frames. FOTV regularization was introduced based on the total variation regularization recovery model, which incorporates the fractional-order differential operator, in order to realize FOTV-regularization-based depth image recovery. These frameworks were used to establish an algorithm for GM-APD depth image recovery based on FOTV. The simulation and experimental results demonstrate that the devised FOTV-recovery algorithm improved the target reduction degree, peak signal–to–noise ratio, and structural similarity index measurement by 76.6%, 3.5%, and 6.9% more than the TV, respectively, in the same SBR and statistic frame conditions. Thus, the devised approach is able to effectively recover GM-APD lidar depth images in low SBR and limited statistic frame conditions.

A Geiger-mode avalanche photodiode (GM-APD) laser radar range image has much noise when the signal-to-background ratios (SBRs) are low, making it difficult to recover the real target scene. In this paper, based on the GM-APD lidar denoising model of fractional-order total variation (FOTV), the spatial relationship and similarity relationship between pixels are obtained by using a spatial kernel function and range kernel function to optimize the fractional differential operator, and a new FOTV GM-APD lidar range-image denoising algorithm is designed. The lost information and range anomalous noise are suppressed while the target details and contour information are preserved. The Monte Carlo simulation and experimental results show that, under the same SBRs and statistical frame number, the proposed algorithm improves the target restoration degree by at least 5.11% and the peak signal-to-noise ratio (PSNR) by at least 24.6%. The proposed approach can accomplish the denoising of GM-APD lidar range images when SBRs are low.