# A Unified Denoising Framework for Restoring the LiDAR Point Cloud Geometry of Reflective Targets
## 1 Introduction  
In recent years, Light Detection and Ranging (LiDAR) technology has undergone rapid development and become a hotspot in both academic research and industrial applications. By emitting pulsed laser beams, LiDAR can quickly capture the three-dimensional spatial information and intensity of surrounding environments. LiDAR demonstrates remarkable advantages under complex scenarios, adverse weather conditions, and varying lighting environments. Consequently, it has been widely used in various applications, such as autonomous driving [1, 2, 3, 4], digital twin city modeling [5, 6, 7], agricultural monitoring [8, 9, 10], and forestry surveying [11, 12, 13]. However, LiDAR systems encounter several critical challenges due to the divergence of the laser beam and the presence of reflective targets (e.g., traffic signs) in complex environments. First, when the laser scans the edges of targets, the signal received by the detector is a mixture of laser echo signals from both the target and the object behind it. This causes the LiDAR system to inaccurately estimate the distance between them, resulting in noise points known as the **veiling effect**[14]. Second, reflective targets can induce abnormal range measurements, introducing range-anomalous points and reducingfeature points on the target surface. Third, the blooming effect [15; 16] generates scattered points around the target, leading to distortions in the geometric shape and dimensions of the target. These challenges significantly degrade the performance of object detection and classification algorithms in autonomous driving applications. Consequently, it is still a critical and challenging task to develop effective point cloud denoising algorithms to restore the geometry of reflective targets. To address these issues, various point cloud denoising methods have been proposed [17; 18], which can be categorized into traditional methods [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32] and deep learning-based methods [33; 34; 35; 36; 37; 38]. Traditional point cloud denoising methods can further be categorized into filter-based and optimization-based methods. Filter-based methods [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29] generally assume that noise is present in high-frequency components and employ filters that function on point positions or normal vectors. The pass-through filter is a simple and effective algorithm in the PCL (Point Cloud Library) [19]; it removes values that are either inside or outside a specified range along a specific dimension (e.g., X, Y, Z coordinates or intensity attribute). [PERSON] [20; 21] improved the computational efficiency of the pass-through filter by optimizing the vector access logic. The statistical filter leverages statistical analysis to remove outliers that are far from their neighbors based on the relative distances between each point and its neighboring points. This method is particularly effective for point clouds with substantial noise or a high presence of outliers. [PERSON] [22] developed two robust statistical methods for detecting outliers in 3D point cloud data: one leveraging robust z-scores and the other utilizing a robust Mahalanobis distance approach. By incorporating local neighborhood information, the two methods effectively identify both clustered and uniformly distributed outliers. [PERSON] [23] introduced an adaptive approach that utilizes point cloud cell subdivision. Rather than generating a single histogram for the entire dataset, the proposed method applies filtering to smaller segments, where variations in ground elevation can be disregarded. The bilateral filter is a technique inspired by the bilateral filter used in image processing, designed to smooth data while preserving edges and geometric features. The method operates by weighting the influence of neighboring points based on both their spatial proximity and feature similarity, such as intensity or surface normal vectors.