# A Unified Denoising Framework for Restoring the LiDAR Point Cloud Geometry of Reflective Targets
## 1 Introduction
[PERSON] [24] proposed a fast and effective anisotropic mesh denoising algorithm that filters mesh vertices along the normal direction using local neighborhoods. Inspired by the success of bilateral filtering in image denoising, the method extends its principles to 3D meshes, addressing the unique challenges of transitioning from 2D images to 3D manifolds. [PERSON] [25] developed a method that adapts the bilateral filter from grayscale images to 3D meshes, denoising points by considering both spatial proximity and normal direction. This approach achieves effective noise reduction while preserving sharp edges. [PERSON] [26] conducted experimental evaluations of the effectiveness of the point cloud bilateral filtering algorithm in automatic driving scenes. The radius filter identifies and removes outliers in a point cloud by evaluating the number of neighboring points within a specified radius, retaining points only if their neighborhood density meets a predefined threshold. [PERSON] [27] introduced a noise-reduction approach to filtering point clouds, utilizing an adaptive radius outlier removal filter that incorporates principal component analysis. [PERSON] [28] developed an algorithm inspired by the ROL (Radius Outlier Filter), designed to detect outliers in large-scale point clouds with a non-exponential time complexity. [PERSON] [29] proposed a multibeam point cloud denoising method that combines radius filtering for edge noise removal with density clustering to restore mistakenly filtered terrain points. However, filter-based denoising algorithms are limited by their reliance on predefined parameters and assumptions, making it challenging to balance noise reduction and feature preservation in complex or diverse point cloud datasets. Optimization-based denoising methods [30; 31; 32] address the problem by formulating it as an optimization task. The goal is to produce a denoised point cloud that closely aligns with the input data while satisfying constraints derived from prior knowledge of the underlying geometry and noise distribution. However, achieving satisfactory results using these methods often requires careful parameter tuning, especially for complex point cloud structures. Deep learning-based methods can be classified into supervised [33; 34; 35] and unsupervised approaches [36; 37; 38], depending on the availability of labeled data during model training. Deep learning-based techniques eliminate these limitations by learning features directly from the data. [PERSON] [34] presented a data-driven approach to denoising unordered point clouds, building on the PCPNet framework. The method removes outliers and computes correction vectors to align noisy points with clean surfaces. [PERSON] [38] proposed an algorithm that builds a model to predict a score for each point, representing its significance and helping to differentiate between noise and valid data. Through iterative processing of the initial point cloud, low-score points (noise) are gradually eliminated, while high-score points are preserved. However, supervised approaches typically require large labeled datasets, which are often difficult to obtain. In contrast, unsupervised methods face challenges such as reliance on assumptions about noise characteristics and a limited ability to generalize across diverse LiDAR point cloud datasets. To remove noise points while preserving features, we developed a Unified Denoising Framework (UDF) for restoring the geometry of reflective targets. The UDF consists of three modules: a veiling effect denoising module, a range anomalies correction module, and a blooming effect denoising module. The performance of the UDF was quantitatively evaluated using a self-constructed traffic sign point cloud dataset. Compared with some traditional and deep learning-based denoising algorithms, the results demonstrated that the proposed framework achieved significant advantages in both denoising performance and geometric feature restoration. Our contribution in this paper can be summarized in the following three aspects:  
1.