Noname manuscript No. (will be inserted by the editor) eSphere: Extracting spheres from unorganized point clouds How to extract multiple spheres accurately and simultaneously Trung-Thien Tran · Van-Toan Cao · Denis Laurendeau Received: date / Accepted: date Abstract Spheres are popular geometric primitives fo- und in many manufactured objects. However, sphere fitting and extraction have not been investigated in depth. In this paper, a robust method is proposed to extract multiple spheres accurately and simultaneously from unorganized point clouds. Moreover, a novel val- idation step is presented to assess the quality of the detected spheres, which helps to remove the confusion between perfect spheres and sphere-like shapes such as ellipsoids and paraboloids. A novel sampling strategy is introduced to reduce computational burden for sphere extraction. Experiments on both synthetic and scanned point clouds with different levels of noise and outliers are conducted and the results compared to state-of-the- art methods. These experiments demonstrate the effi- ciency and robustness of the proposed sphere extraction method. Keywords Sphere fitting; Sphere extraction; Sphere validation; Mean Shift Clustering; 1 Introduction Spheres are popular primitives found in manufactured objects and even in biochemistry models, as shown in Fig. 1. Moreover, spheres have many applications such as RoboCup games [1], reverse engineering [2, 3], med- ical imaging [4], etc. Especially sphere markers were used extensively for monocular or RGB-D camera and laser scanner calibration [5–9] in which robust sphere estimation is necessary to achieve good results. Many Department of Electrical and Computer Engineering, Laval University, Quebec G1V-0A6, Canada trung-thien.tran.1@ulaval.ca,van-toan.cao.1@ulaval.ca, denis.laurendeau@gel.ulaval.ca metrology and engineering applications (reverse engi- neering, part-to-CAD analysis) also require that spheres are extracted automatically and reliably from meshes or point clouds. However sphere extraction from 3D data has not yet been investigated as thoroughly as plane [10–12] and cylinder [13, 14] extraction. There is thus a need for robust and computationally efficient ap- proaches for sphere extraction. More specifically, meth- ods have been proposed for sphere fitting and extrac- tion from 3D point clouds [7, 15–18]. However, valida- tion methods for assessing the validity and reliability of extracted spheres remain scarce. Among the above approaches, hierarchical cluster- ing [15, 19] cannot be applied for sphere detection only, because all primitives (plane, cylinder and sphere) must be processed simultaneously to create a global cluster- Five balls captured by Kinect Sphere kits for FARO Focus3D and Trimble TX5 Biochemistry models CAD models Fig. 1. Spheres exist in different types of models such as CAD, games, biochemistry and commercial sphere kits for FARO and TRIMBLE scanners.