Objective Three-dimensional (3D) images provide a stereoscopic view enabling observers to perceive shapes, sizes, and spatial relationships. They play an important role in a variety of applications including computer vision, medical imaging, robotics, autonomous driving, graphics, virtual reality (VR) and augmented reality (AR). 3D range gated imaging (Gated3D) is a light ranging and imaging (LiRAI) technique, which can obtain high-resolution 3D spatial images as well as 2D intensity images, avoiding the heterogeneous data fusion problem in the combined technology of LiDAR and camera. Gated3D can utilize at least two gated images to recover depth information. Similar to existing LiDAR, Gated3D is also influenced by device noise, temporal characteristics, target reflectivity and background environment, which results in a low peak signal-to-noise ratio (PSNR) of 3D images, ultimately affecting practical applications. To improve the PSNR of the LiRAI based on Gated3D, we propose a trilateral filter smoothing and denoising algorithm.

Methods For the gated LiRAI, the smoothing and denoising algorithm of trilateral filter utilizes spatial and range filtering in 3D images, as well as the grayscale value filtering in gated images. The trilateral filter is explained with the Eq.(1), and the spatial, range and gray-scale filtering are shown in Eq.(2)-(5). Compared to the traditional bilateral filtering algorithm, the trilateral filtering algorithm introduces grayscale value filtering. For depth maps with high noise recovered by the gated LiRAI, the proposed algorithm can preserve the object edge information while smoothing small-scale noise, even if two objects with different reflectance are relatively close together. After smoothing noise, the depth maps are transformed to point cloud, and the statistical outlier removal (SOR) algorithm is used to remove outliers in the point cloud.

Results and Discussions The trilateral filter algorithm is tested on both simulated data and real-world data. In the simulation experiment, we designed a pyramid-shaped depth map to simulate the smooth regions and edge regions. The original pyramid-shaped depth maps and their depth maps with different noise are shown in Fig.3. We test bilateral filter and trilateral filter algorithms by applying them to smooth the noise in the pyramid-shaped depth maps, and the PSNR of the whole depth map as well as the edge regions of the depth map are analyzed. The results are shown (Fig.5-6, Tab.1-2). Two diffuse targets with different reflectivity are used as the real-world test data in Fig.7, and a part of the data are selected for quantitative analysis in Fig.9. The results are shown in Tab.3. In both test datasets, the trilateral filter algorithm performs better than the bilateral filter algorithm especially in the edge regions. The result of real scene by the proposed algorithm are shown in Fig.10.

Conclusions We propose a noise smoothing algorithm of trilateral filter to smooth noise in 3D images from gated LiRAI, and further combine the SOR filter algorithm to remove outliers in point cloud. The 3D images recovered by the LiRAI based on Gated3D are affected by noise, in which case the traditional noise smoothing algorithm such as the bilateral filter is unable to smooth the noise and preserve edges. The proposed algorithm can preserve the edges when the targets have different reflectivity, and performs better than the bilateral filter algorithm on both synthetic data and real-scene data.