With the advancement of 3D scanning technologies, point clouds have become fundamental for representing 3D spatial data, with applications that span across various scientific and technological fields. Practical analysis of this data depends crucially on available neighborhood descriptors to accurately characterize the local geometries of the point cloud. This paper introduces LitS, a novel neighborhood descriptor for 2D and 3D point clouds. LitS are piecewise constant functions on the unit circle that allow points to keep track of their surroundings. Each element in LitS' domain represents a direction with respect to a local reference system. Once constructed, evaluating LitS at any given direction gives us information about the number of neighbors in a cone-like region centered around that same direction. Thus, LitS conveys a lot of information about the local neighborhood of a point, which can be leveraged to gain global structural understanding by analyzing how LitS changes between close points. In addition, LitS comes in two versions ('regular' and 'cumulative') and has two parameters, allowing them to adapt to various contexts and types of point clouds. Overall, they are a versatile neighborhood descriptor, capable of capturing the nuances of local point arrangements and resilient to common point cloud data issues such as variable density and noise.

翻译：随着三维扫描技术的进步，点云已成为表示三维空间数据的基础，其应用跨越多个科学与技术领域。对此类数据的实际分析在很大程度上依赖于可用的邻域描述符，以准确表征点云的局部几何特征。本文介绍了一种用于二维和三维点云的新型邻域描述符LitS。LitS是定义在单位圆上的分段常数函数，使点能够追踪其周围环境。LitS定义域中的每个元素代表相对于局部参考系的一个方向。构建完成后，在任何给定方向上评估LitS，即可获取以该方向为中心的锥状区域内邻点的数量信息。因此，LitS传递了点的局部邻域的大量信息，通过分析相邻点之间LitS的变化规律，可进一步获取全局结构理解。此外，LitS提供“常规”与“累积”两种版本，并包含两个可调参数，使其能适应不同应用场景与点云类型。总体而言，LitS是一种多功能的邻域描述符，既能捕捉局部点集分布的细微特征，又能有效应对点云数据中常见的密度不均与噪声干扰等问题。