LitS: A novel Neighborhood Descriptor for Point Clouds

TL;DR

LitS introduces a novel neighborhood descriptor for 2D and 3D point clouds that encodes local angular structure by modeling neighbors as illuminating sources on directional arcs. It defines regular LitS and cumulative LitS on directional domains, with parameters $\lambda$ and $\varphi$ controlling illumination, and extends the construction to 3D via spherical caps on a chosen plane. The paper analyzes meanings, invariances, and surroundedness associated with LitS, and demonstrates practical use in interior/boundary detection, corner/line neighborhood analysis, and visualization, while discussing limitations and future directions such as compact representations and ML integration. Together, these contributions offer a robust, geometry-informed tool for local neighborhood understanding and global structure inference in point clouds.

Abstract

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.

Figures (19)

• Figure 1: Circular arc lit up by $q$.
• Figure 2: Illuminating neighborhood $Q_\lambda$ on the left, with the corresponding plot of LitS and cumulative LitS on the right (dash-dot line and solid line styles, respectively).
• Figure 3: Circular arc lit up by $q$ in terms of $\varphi$. Case $\varphi<\pi/2$ on the left, and $\varphi>\pi/2$ on the right. The values used are $\varphi=\pi/3$ and $\varphi=5\pi/7$, respectively.
• Figure 4: $\omega(\varphi)$ with $r_p/r_q$ ranging from $1$ (red) to $0$ (blue) in increments of $0.1$, colored using the Jet colormap.
• Figure 5: LitS' construction along a plane given by $n$.