PGP2X: Principal Geometric Primitives Parameters Extraction

Zahra Toony, Denis Laurendeau, Christian Gagné


In reverse engineering, it is important to extract the 3D geometric primitives that compose an object. It is also important to find the values of the parameters describing each primitive. This paper presents an approach for the estimation of the parameters of geometric primitives once their type is known using 3D information. The primitives of interest are planes, spheres, cylinders, cones, tori and partial instances of the latter four types. The proposed approach extends methods found in the literature for planes, spheres, cylinders and cones and proposes a new method for dealing with tori. The results of the proposed method are compared to approaches found in the literature as well as with ground truth values. The proposed method can be applied to the estimation of parameters of geometric primitives of synthetic CAD models as well as for models of real objects acquired with 3D scanners.


  1. Attene, M., Falcidieno, B., and Spagnuolo, M. (2006). Hierarchical mesh segmentation based on fitting primitives. The Visual Computer, 22(3):181-193.
  2. Attene, M. and Patanè, G. (2010). Hierarchical structure recovery of point-sampled surfaces. In Computer Graphics Forum, volume 29, pages 1905-1920. Wiley Online Library.
  3. Benko, P., Kós, G., Várady, T., Andor, L., and Martin, R. (2002). Constrained fitting in reverse engineering. Computer Aided Geometric Design, 19(3):173-205.
  4. Bolles, R. C. and Fischler, M. A. (1981). A RANSAC-based approach to model fitting and its application to finding cylinders in range data. In 7th Int. Joint Conf. on Artificial Intelligence (IJCAI'81), volume 1981, pages 637-643.
  5. Borrmann, D., Elseberg, J., Lingemann, K., and Nüchter, A. (2011). The 3D Hough transform for plane detection in point clouds: A review and a new accumulator design. 3D Research, 2(2):1-13.
  6. Chaperon, T., Goulette, F., and Laurgeau, C. (2001). Extracting cylinders in full 3D data using a random sampling method and the gaussian image. In Proc. of the Vision Modelling and Visualization Conf., volume 1, pages 35-42. Citeseer.
  7. Chen, T.-C. and Chung, K.-L. (2001). An efficient randomized algorithm for detecting circles. Computer Vision and Image Understanding, 83(2):172-191.
  8. Chernov, N. (2009). Circle Fitting by Taubin method. http:// 22678-circle-fit-taubin-method-. [Online; accessed January-2009].
  9. Cohen-Steiner, D., Alliez, P., and Desbrun, M. (2004). Variational shape approximation. In ACM Trans. on Graphics (TOG), volume 23, pages 905-914.
  10. Fayolle, P.-A. and Pasko, A. (2013). Segmentation of discrete point clouds using an extensible set of templates. The Visual Computer, 29(5):449-465.
  11. Fischler, M. A. and Bolles, R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-395.
  12. Garland, M., Willmott, A., and Heckbert, P. S. (2001). Hierarchical face clustering on polygonal surfaces. In Proc. of the 2001 Sym. on Interactive 3D graphics, pages 49-58. ACM.
  13. Johnston, J. D. (1988). Transform coding of audio signals using perceptual noise criteria. IEEE Journal on Selected Areas in Communications, 6(2):314-323.
  14. Kasa, I. (1976). A circle fitting procedure and its error analysis. IEEE Trans. on Instrumentation and Measurement, 1001(1):8-14.
  15. Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. (2003). Rotation invariant spherical harmonic representation of 3D shape descriptors. In Proc. of the 2003 Eurographics/ACM SIGGRAPH Sym. on Geometry processing, pages 156-164. Eurographics Association.
  16. Kotthäuser, T. and Mertsching, B. (2012). Triangulationbased plane extraction for 3D point clouds. In Intelligent Robotics and Applications, pages 217-228. Springer.
  17. Li, Y., Wu, X., Chrysathou, Y., Sharf, A., Cohen-Or, D., and Mitra, N. J. (2011). Globfit: Consistently fitting primitives by discovering global relations. In ACM Transactions on Graphics, volume 30, page 52.
  18. Liu, Y.-J., Zhang, J.-B., Hou, J.-C., Ren, J.-C., and Tang, W.-Q. (2013). Cylinder detection in large-scale point cloud of pipeline plant. IEEE Trans. on Visualization and Computer Graphics, 19(10):1700-1707.
  19. Lozano-Perez, T., Grimson, W., and White, S. (1987). Finding cylinders in range data. In Proc. of IEEE Intl. Conf. on Robotics and Automation, volume 4, pages 202-207.
  20. LSGE (2004). LSGE: The Least Squares Geometric Elements Library. key_functions/fitting_routines/.
  21. Lukács, G., Martin, R., and Marshall, D. (1998). Faithful least-squares fitting of spheres, cylinders, cones and tori for reliable segmentation. In 5th European Conf. on Computer Vision (ECCV'98), pages 671- 686. Springer.
  22. Olson, C. F. (2001). Locating geometric primitives by pruning the parameter space. Pattern Recognition, 34(6):1247-1256.
  23. Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D. (2002). Shape distributions. ACM Transactions on Graphics (TOG), 21(4):807-832.
  24. Pratt, V. (1987). Direct least-squares fitting of algebraic surfaces. ACM SIGGRAPH Computer Graphics, 21(4):145-152.
  25. Rabbani, T. and Van Den Heuvel, F. (2005). Efficient Hough transform for automatic detection of cylinders in point clouds. Proc. of ISPRS WS on Laser Scanning, 3:60-65.
  26. Scales, L. (1985). Introduction to non-linear optimization. Springer-Verlag New York, Inc.
  27. Schmitt, S. R. (2005). Center and Radius of a Sphere from Four Points. zenosamples/zs_sphere4pts.html.
  28. Schnabel, R., Wahl, R., and Klein, R. (2007). Efficient RANSAC for point-cloud shape detection. In Computer graphics forum, volume 26, pages 214-226. Wiley Online Library.
  29. Taubin, G. (1991). Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 13(11):1115-1138.
  30. Toony, Z., Laurendeau, D., and Gagné, C. (2014). Recognizing 3D principal primitives using gaussian sphere and gaussian accumulator. Internal Report. Computer Vision and System Laboratory, Laval University, August 2014.
  31. Zhang, J., Cao, J., Liu, X., Wang, J., Liu, J., and Shi, X. (2013). Point cloud normal estimation via lowrank subspace clustering. Computers & Graphics, 37(6):697-706.
  32. Zhu, K., Wong, Y. S., Loh, H. T., and Lu, W. F. (2012). 3D CAD model retrieval with perturbed laplacian spectra. Computers in Industry, 63(1):1-11.

Paper Citation

in Harvard Style

Toony Z., Laurendeau D. and Gagné C. (2015). PGP2X: Principal Geometric Primitives Parameters Extraction . In Proceedings of the 10th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2015) ISBN 978-989-758-087-1, pages 81-93. DOI: 10.5220/0005356400810093

in Bibtex Style

author={Zahra Toony and Denis Laurendeau and Christian Gagné},
title={PGP2X: Principal Geometric Primitives Parameters Extraction},
booktitle={Proceedings of the 10th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2015)},

in EndNote Style

JO - Proceedings of the 10th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2015)
TI - PGP2X: Principal Geometric Primitives Parameters Extraction
SN - 978-989-758-087-1
AU - Toony Z.
AU - Laurendeau D.
AU - Gagné C.
PY - 2015
SP - 81
EP - 93
DO - 10.5220/0005356400810093