Toward Point Cloud Density Consistency in Mobile Laser Scanning: A Mathematical Modeling and Correction Method

Mobile laser scanning (MLS) systems enable rapid acquisition of high-definition 3D point clouds for urban digitization, topographic mapping, and infrastructure inspection. Despite the critical role of point cloud density in quantifying data fidelity and object discriminability, its inherent spatiotemporal variability — arising from the nonlinear interplay of scanning geometry, platform dynamics, and surface topology — has remained inadequately addressed in current metrological frameworks. This study establishes a rigorous mathematical model that quantifies MLS density variations through the interdependent variables: density search radius, scanning distance, angular resolution, platform velocity, pulse repetition frequency, and three angles defining the spatial orientation of the local infinitesimal plane at the target point. Building upon this formulation, we propose the first MLS point cloud density correction method to mitigate heterogeneity caused by varying influencing factors and to derive a new corrected density value for each point that serves as an indicator of target geometry attribute. Experiments conducted across different platforms and environments demonstrate that the proposed method effectively eliminates inhomogeneity in density. The correction procedure achieves an average 61% decrease in the density coefficient of variation over homogeneous surfaces. The proposed method exhibits strong performance regarding feasibility and generality, offering significant application value in enhancing MLS data interpretation and understanding spatial distribution patterns of point clouds under various circumstances.