Abstract
Due to recent advances in high-speed 3D laser-scanning technologies, the set of dense points collected from the external boundary surface of a physical object, often referred to as the point cloud data, is emerging as a new representation format of 3D shapes. A typical point cloud data set contains millions of coordinate data points, and this leads to significant computational challenges for the subsequent data processing tasks in practical applications. This paper presents a new point cloud simplification algorithm to reduce the number of data points scanned from a mechanical part, in which the boundary surfaces often contain sharp edges. Because of the distinct feature represented by data points located on or near the sharp edges (edge points), these points should always be retained by the simplification process. The proposed algorithm thus identifies these edge points first and then progressively removes the least important data point until the specified data reduction ratio is reached. The quantification of a point’s importance is based on points in its neighborhood and corresponds to the point’s contribution to the representation of local surface geometry. The effectiveness of the proposed algorithm is demonstrated through the simplification results of several practical point cloud data sets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Varady T, Martin RR, Cox J (1997) Reverse engineering of geometric models—an introduction. Computer-Aided Des 29(4):255–268 doi:10.1016/S0010-4485(96)00054-1
Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. In: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’87), pp. 163–169
Fleishman S, Cohen-Or D, Alexa M, Silva CT (2003) Progressive point set surfaces. ACM Trans Graph 22(4):997–1011 doi:10.1145/944020.944023
Amenta N, Kil YJ (2004) Defining point-set surfaces. ACM Trans Graph 23(3):264–270 doi:10.1145/1015706.1015713
Hoschek J, Dietz U, Wilke W (1997) A geometric concept of reverse engineering of shape: approximation and feature lines. In: Proceedings of the International Conference on Mathematical Methods for Curves and Surfaces II, Lillehammer, Norway, pp. 253–262
Pauly M, Gross M, Kobbelt LP (2002) Efficient simplification of point-sampled surfaces. In: Proceedings of the 13th IEEE Visualization Conference, Boston, MA, pp 163–170
Luebke DP (2001) A developer’s survey of polygonal simplification algorithms. IEEE Comput Graph Appl 21(3):24–35 doi:10.1109/38.920624
Cignoni P, Montani C, Scopigno R (1998) A comparison of mesh simplification algorithms. Comput Graph 22(1):37–54 doi:10.1016/S0097-8493(97)00082-4
Pauly M, Gross M (2001) Spectral processing of point-sampled geometry. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’01), pp. 379–386
Moenning C, Dodgson NA (2004) Intrinsic point cloud simplification. In: Proceedings of the 14th International Conference on Computer Graphics and Vision (GraphiCon), Moscow, Russia
Eldar Y, Lindenbaum M, Porat M, Zeevi YY (1997) The farthest point strategy for progressive image sampling. IEEE Trans Image Process 6(9):1305–1315 doi:10.1109/83.623193
Linsen L (2001) Point cloud representation. Technical Report, Faculty of Informatics, University of Karlsruhe, Germany
Alexa M, Behr J, Cohen-Or D, Fleishman S, Levin D, Silva CT (2001) Point set surfaces. In: Proceedings of the IEEE Conference on Visualization (VIS’01), pp. 21–28
Levin D (2004) Mesh-independent surface interpolation. In: Brunnett G, Hamann B, Muller H, Linsen L (eds.) Geometric Modeling for Scientific Visualization, Springer, pp. 37–49
Kalaiah A, Varshney A (2003) Modeling and rendering of points with local geometry. IEEE Trans Vis Comput Graph 9(1):30–42 doi:10.1109/TVCG.2003.1175095
Lee KH, Woo H, Suk T (2001) Point data reduction using 3D grids. Int J Adv Manuf Technol 18(3):201–210 doi:10.1007/s001700170075
Demarsin K, Vanderstraeten D, Volodine T, Roose D (2007) Detection of closed sharp edges in point clouds using normal estimation and graph theory. Computer-Aided Des 39(3):276–283 doi:10.1016/j.cad.2006.12.005
Song H, Feng HY, OuYang D (2008) Automatic detection of tangential discontinuities in point cloud data. ASME J Comput Inf Sci Eng 8(2):021001:1–10
OuYang D, Feng HY (2005) On the normal vector estimation for point cloud data from smooth surfaces. Computer-Aided Des 37(10):1071–1079 doi:10.1016/j.cad.2004.11.005
Boissonnat JD, Devillers O, Pion S, Teillaud M, Yvinec M (2002) Triangulations in CGAL. Comput Geom Theory Appl 22(1–3):5–19
Devillers O, Teillaud M (2003) Perturbations and vertex removal in a 3D Delaunay triangulation. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 313–319
Song H, Feng HY (2008) A global clustering approach to point cloud simplification with a specified data reduction ratio. Computer-Aided Des 40(3):281–292
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Song, H., Feng, HY. A progressive point cloud simplification algorithm with preserved sharp edge data. Int J Adv Manuf Technol 45, 583–592 (2009). https://doi.org/10.1007/s00170-009-1980-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-009-1980-4