Eigen-feature analysis of weighted covariance matrices for LiDAR point cloud classification

The features used in the separation of different objects are important for successful point cloud classification. Eigen-features from a covariance matrix of a point set with the sample mean are commonly used geometric features that can describe the local geometric characteristics of a point cloud and indicate whether the local geometry is linear, planar, or spherical. However, eigen-features calculated by the principal component analysis of a covariance matrix are sensitive to LiDAR data with inherent noise and incomplete shapes because of the non-robust statistical analysis. To obtain reliable eigen-features from LiDAR data and to improve classification accuracy, we introduce a method of analyzing local geometric characteristics of a point cloud by using a weighted covariance matrix with a geometric median. Each point is assigned a weight to represent its spatial contribution in the weighted principal component analysis and to estimate the geometric median which can be regarded as a localized center of a shape. In the experiments, qualitative and quantitative analyses on airborne LiDAR data and simulated point clouds show a clear improvement of the proposed method compared with the standard eigen-features. The classification accuracy is improved by 1.6-4.5% using a supervised classifier.