LiDAR point clouds, representing detailed three-dimensional descriptions of natural and built environments, are widely used in applications such as updating digital elevation models, monitoring glaciers and landslides, shoreline analysis, and urban development. A crucial step in these applications is the classification of 3D LiDAR points into semantic categories such as vegetation, man-made structures, and water. In our previous work [5], we introduced product coefficients as measure-theoretic descriptors that enrich LiDAR data with local structural information. Computed on dyadic neighborhoods around each point, these coefficients capture geometric variability beyond raw spatial coordinates.

In this paper, we address the enhancement of classification accuracy for 3D point cloud Lidar data, an optical remote sensing technique that estimates the three-dimensional coordinates of a given terrain. Our approach introduces product coefficients, theoretical quantities derived from measure theory, as additional features in the classification process. We define and present the formulation of these product coefficients and conduct a comparative study, using them alongside principal component analysis (PCA) as feature inputs. Results demonstrate that incorporating product coefficients into the feature set significantly improves classification accuracy within this new framework.