Many of the point cloud processing techniques have their origin in image processing. But mathematical morphology, despite being one of the most used image processing techniques, has not yet been clearly adapted to point clouds. The aim of this work is to design the basic operations of mathematical morphology applicable to 3D point cloud data, without the need to transform point clouds to 2D or 3D images and avoiding the associated problems of resolution loss and orientation restrictions. The object shapes in images, based on pixel values, are assumed to be the existence or absence of points, therefore, morphological dilation and erosion operations are focused on the addition and removal of points according to the structuring element. The structuring element, in turn, is defined as a point cloud with characteristics of shape, size, orientation, point density, and one reference point. The designed method has been tested on point clouds artificially generated, acquired from real case studies, and the Stanford bunny model. The results show a robust behaviour against point density variations and consistent with image processing equivalent. The proposed method is easy and fast to implement, although the selection of a correct structuring element requires previous knowledge about the problem and the input point cloud. Besides, the proposed method solves well-known point cloud processing problems such as object detection, segmentation, and gap filling.@en

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.

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This work presents an approach to automatically detect structural floor elements such as steps or ramps in the immediate environment of buildings, elements that may affect the accessibility to buildings. The methodology is based on Mobile Laser Scanner (MLS) point cloud and trajectory information. First, the street is segmented in stretches along the trajectory of the MLS to work in regular spaces. Next, the lower region of each stretch (the ground zone) is selected as the ROI and normal, curvature and tilt are calculated for each point. With this information, points in the ROI are classified in horizontal, inclined or vertical. Points are refined and grouped in structural elements using raster process and connected components in different phases for each type of previously classified points. At last, the trajectory data is used to distinguish between road and sidewalks. Adjacency information is used to classify structural elements in steps, ramps, curbs and curb-ramps. The methodology is tested in a real case study, consisting of 100 m of an urban street. Ground elements are correctly classified in an acceptable computation time. Steps and ramps also are exported to GIS software to enrich building models from Open Street Map with information about accessible/inaccessible entrances and their locations.@en