LitS: A novel Neighborhood Descriptor for Point Clouds

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.

💡 Research Summary

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The paper introduces LitS (Light‑up Structure), a novel local descriptor for both 2‑D and 3‑D point clouds that encodes the angular distribution of a point’s neighbors as piecewise‑constant functions on the unit circle (or on a great circle of the unit sphere). The construction begins by defining a neighborhood Q around a query point p and a scaling factor λ ∈ (0, 1] that determines an inner radius rₚ = λ·r_Q, where r_Q is the maximum distance of any neighbor in Q. Neighbors closer than rₚ are ignored, while the remaining “illuminating” neighbors q ∈ Q_λ are treated as light sources that illuminate a circular arc on the boundary of the disc of radius rₚ. In 2‑D, the illuminated arc a(q) is derived from a right‑triangle geometry and expressed as (θ_q − arccos(rₚ/r_q), θ_q + arccos(rₚ/r_q)). A second parameter φ (0 < φ ≤ π) generalizes the arc length by limiting the incidence angle of the illuminating ray; the arc half‑width becomes ω = φ − arcsin((rₚ/r_q)·sin φ).

Two versions of LitS are defined:

• Regular LitS Lₚ