Mathematical morphology directly applied to point cloud data

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.