Local geometric descriptors for multi-scale probabilistic point classification of airborne LiDAR point clouds

Abstract

Point classification is necessary for detection and extraction of geometric feature (folds, creases, junctions, surfaces), and subsequent 3D reconstruction of point-sampled geometry of topographic data captured using airborne LiDAR technology. Geometry-based point classification (line-, surface-, point-type features) is determined using shape of the local neighborhood, given by the local geometric descriptor (LGD) at every point in the point cloud. Covariance matrix of local neighborhoods is the conventionally used LGD in the LiDAR community. However, it is known that covariance analysis has drawbacks in detection of sharp features, which are a subset of the line-type features. Here, we compare the performance of new variants of existing LGDs, such as weighted covariance matrix, and that based on tensor voting concept, in geometric classification with that of covariance matrix. We propose a multi-scale probabilistic saliency map based on eigenvalues of the LGDs for computing the classification. Usually the state-of-the-art performance analyses of LGDs in the classification outcomes are done downstream after feature extraction. We propose that the comparisons may be done upstream at the classification stage itself, which can be achieved by expressing these LGDs as positive semidefinite second-order tensors. We perform qualitative comparisons of the tensor fields based on shape and orientation of the tensors, and the classification outcomes using visualizations. We visualize LGDs using superquadric tensor glyphs and point rendering, using our proposed saliency map as colormap. Our detailed comparative analysis shows that the new variant of LGDs based on tensor voting classify line-type features, especially sharp features, better than covariance-based LGDs. Our proposed LGD based on tensor voting performs better than the covariance matrix, for our goal of detecting sharp features, e.g. gabled roofs in buildings.