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Automatic curb detection is an important issue in road maintenance, three-dimensional (3D) urban modeling, and autonomous navigation fields. This paper is focused on the segmentation of curbs and street boundaries using a 3D point cloud captured by a mobile laser scanner (MLS) system. Our method provides a solution based on the projection of the measured point cloud on the XY plane. Over that plane, a segmentation algorithm is carried out based on morphological operations to determine the location of street boundaries. In addition, a solution to extract curb edges based on the roughness of the point cloud is proposed. The proposed method is valid in both straight and curved road sections and applicable both to laser scanner and stereo vision 3D data due to the independence of its scanning geometry. The proposed method has been successfully tested with two datasets measured by different sensors. The first dataset corresponds to a point cloud measured by a TOPCON sensor in the Spanish town of Cudillero. The second dataset corresponds to a point cloud measured by a RIEGL sensor in the Austrian town of Horn. The extraction method provides completeness and correctness rates above 90% and quality values higher than 85% in both studied datasets.