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Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

We first introduce a surface normal estimation procedure for point clouds capable of handling geometric singularities in the data, such as edges and corners. Our formulation is based on recasting the popular Principal Component Analysis (PCA) method as a constrained nonlinear least squares (NLSQ) problem. In contrast to traditional PCA, the new formulation assigns appropriate weights to neighboring points automatically during the optimization process in order to minimize the contributions of points located across singularities. We extend this strategy to point cloud denoising by combining normal estimation, point projection, and declustering into one NLSQ formulation. Finally, we propose a point cloud segmentation technique based on surface normal estimates and local point connectivity. In addition to producing consistently oriented surface normals, the process segments the point cloud into disconnected components that can each be segmented further into piecewise smooth components as needed.

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References

  1. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph. 9, 3–15 (2003)

    Article  Google Scholar 

  2. Amenta, N., Bern, M.: Surface reconstruction by voronoi filtering. In: Proceedings of the Fourteenth Annual Symposium on Computational Geometry. ACM, New York (1998)

    Google Scholar 

  3. Azariadis, P.: Parameterization of clouds of unorganized points using dynamic base surfaces. Comput. Aided Des. 36, 607–623 (2004)

    Article  Google Scholar 

  4. Besl, P.J., Jain, R.C.: Segmentation through variable-order surface fitting. IEEE Trans. Pattern Anal. Mach. Intell. 10, 167–192 (1988)

    Article  Google Scholar 

  5. Boissonnat, J.D., Cazals, F.: Smooth surface reconstruction via natural neighbor interpolation of distance functions. In: Proceedings of 16th Annual Symposium on Computational Geometry, pp. 223–232. ACM, New York (2000)

    Google Scholar 

  6. Calderon, F., Ruiz, U., Rivera, M.: Surface-normal estimation with neighborhood reorganization for 3d reconstruction. In: Proceedings of the Congress on Pattern Recognition 12th Iberoamerican Conference on Progress in Pattern Recognition, Image Analysis and Applications, pp. 321–330. Springer, Berlin/Heidelberg (2007)

    Google Scholar 

  7. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986)

    Article  Google Scholar 

  8. Demarsin, K., Vanderstraeten, D., Volodine, T., Roose, D.: Detection of closed sharp edges in point clouds using normal estimation and graph theory. Comput. Aided Des. 39, 276–283 (2007)

    Article  Google Scholar 

  9. Dey, T.K., Goswami, S.: Provable surface reconstruction from noisy samples. Comput. Geom. Theory Appl. 35, 124–141 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dey, T., Sun, J.: Normal and feature approximations from noisy point clouds. In: FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science, vol. 4337, pp. 21–32. Springer, Berlin/Heidelberg (2006)

    Google Scholar 

  11. Dey, T.K., Li, G., Sun, J.: Normal estimation for point clouds: a comparison study for a voronoi based method. In: Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, vol. 0, pp. 39–46 (2005)

    Article  Google Scholar 

  12. Fleishman, S., Drori, I., Cohen-or, D.: Bilateral mesh denoising. ACM Trans. Graph. 22, 950–953 (2003)

    Article  Google Scholar 

  13. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of ACM Siggraph, pp. 71–78. ACM, New York (1992)

    Google Scholar 

  14. Hu, S., Wallner, J.: A second order algorithm for orthogonal projection onto curves and surfaces. Comput. Aided Graph. Des. 22(3), 251–260 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang, J., Menq, C.-H.: Automatic data segmentation for geometric feature extraction from unorganized 3-D coordinate points. IEEE Trans. Robot. Autom. 17, 268–278 (2001)

    Article  Google Scholar 

  16. Huang, H., Li, D., Zhang, H., Ascher, U., Cohen-Or, D.: Consolidation of unorganized point clouds for surface reconstruction. ACM Trans. Graph. 28, 176:1–176:7 (2009)

    Google Scholar 

  17. Huber, P.J.: Robust Statistics. Wiley, New York (2004)

    Google Scholar 

  18. Klasing, K., Althoff, D., Wollherr, D., Buss, M.: Comparison of surface normal estimation methods for range sensing applications. In: IEEE International Conference on Robotics and Automation, 2009. ICRA ’09. IEEE, Piscataway (2009)

    Google Scholar 

  19. Lee, Y., Park, S., Jun, Y., Choi, W.C.: A robust approach to edge detection of scanned point data. Int. J. Adv. Manuf. Technol. 23, 263–271 (2004)

    Article  Google Scholar 

  20. Leung, S., Zhao, H.: A grid based particle method for evolution of open curves and surfaces. J. Comput. Phys. 228, 2993–3024 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lipman, Y., Cohen-Or, D., Levin, D., Tal-Ezer, H.: Parameterization-free projection for geometry reconstruction. ACM Trans. Graph. 26, Article no 22 (2007)

    Google Scholar 

  22. Liu, Y.S., Paul, J.C., Yong, J.H., Yu, P.Q., Zhang, H., Sun, J.G., Ramani, K.: Automatic least-squares projection of points onto point clouds with applications in reverse engineering. Comput. Aided Des. 38, 1251–1263 (2006)

    Article  Google Scholar 

  23. Mitra, N., Nguyen, A., Guibas, L.: Estimating surface normals in noisy point cloud data. In: Spec. Issue Int. J. Comput. Geom. Appl. 14, 261–276 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. OuYang, D., Feng, H.-Y.: On the normal vector estimation for point cloud data from smooth surfaces. Comput. Aided Des. 37, 1071–1079 (2005)

    Article  Google Scholar 

  25. Pauly, M., Gross, M., Kobbelt, L.P.: Efficient simplification of point-sampled surfaces. In: Proceedings of the conference on Visualization 2002. VIS 2002. IEEE Computer Society, Washington, DC (2002)

    Google Scholar 

  26. Pauly, M., Keiser, R., Gross, M.: Multi-scale feature extraction on point-sampled surfaces. Comput. Graph. Forum 22, 281–289 (2003)

    Article  Google Scholar 

  27. Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M.: Shape modeling with point-sampled geometry. ACM Trans. Graph. 22, 641–650 (2003)

    Article  Google Scholar 

  28. Rabbani, T., Van Den Heuvel, F., Vosselmann, G.: Segmentation of point clouds using smoothness constrain. ISPRS Comm. V Symp. Image Eng. Vis. Metrol. 36, 248–253 (2006)

    Google Scholar 

  29. Schmaltz, C., Gwosdek, P., Bruhn, A., Weickert, J.: Electrostatic halftoning. Comput. Graph. Forum 29, 2313–2327 (2010)

    Article  Google Scholar 

  30. Vosselman, G.: Advanced point cloud processing. In: Fritsch, D. (ed.) Photogrammetric Week ’09, pp. 137–146. Wichmann, Heidelberg (2009)

    Google Scholar 

  31. Vosselman, G., Gorte, B., Rabbani, T., Sithole, G.: Recongnising structure in laser scanner point clouds. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 46, 33–38 (2004)

    Google Scholar 

  32. Yang, M., Lee, E.: Segmentation of measured point data using parametric quadric surface approximation. Computer A 31, 449–457 (1999)

    Article  MATH  Google Scholar 

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Acknowledgements

The authors acknowledge ARO/MURI award W911NF-07-1-0185 and NGA NURI Award HM1582-10-1-0012 for support with this work.

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Authors and Affiliations

  1. Department of Radiation Oncology, University of Texas, MD Anderson Cancer Center, Houston, TX, USA

    Edward Castillo

  2. Department of Computational and Applied Mathematics, Rice University, Houston, TX, USA

    Edward Castillo

  3. Department of Mathematics, University of California, Irvine, CA, USA

    Jian Liang & Hongkai Zhao

Authors
  1. Edward Castillo
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  2. Jian Liang
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  3. Hongkai Zhao
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Corresponding author

Correspondence to Edward Castillo .

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Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Castillo, E., Liang, J., Zhao, H. (2013). Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_13

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