Accessibility diagnosis of as-built urban environments is essential for path planning, especially in case of people with reduced mobility and it requires an in-depth knowledge of ground elements. In this paper, we present a new approach for automatically detect and classify urban ground elements from 3D point clouds. The methodology enables a high level of detail classification from the combination of geometric and topological information. The method starts by a planar segmentation followed by a refinement based on split and merge operations. Next, a feature analysis and a geometric decision tree are followed to classify regions in preliminary classes. Finally, adjacency is studied to verify and correct the preliminary classification based on a comparison with a topological graph library. The methodology is tested in four real complex case studies acquired with a Mobile Laser Scanner Device. In total, five classes are considered (roads, sidewalks, treads, risers and curbs). Results show a success rate of 97% in point classification, enough to analyse extensive urban areas from an accessibility point of view. The combination of topology and geometry improves a 10% to 20% the success rate obtained with only the use of geometry.