POINT CLOUD DENOISING USING ROBUST PRINCIPAL COMPONENT ANALYSIS

Esmeide A. Leal Narváez, Nallig Eduardo Leal Narváez

Abstract

This paper presents a new method for filtering noise occurring in point cloud sampled data. The method smoothes the data set whereas preserves sharp features. We propose a new weighted variant of the principal component analysis method, which instead of using exponential weighting factors inversely proportional to the Euclidean distance to the mean, which is computationally expensive, uses weighting factors assignment by inversely proportional repartition of the sum of distance to the mean. The determination of weighted factors by means of inverse proportional repartition makes our variant robust to outliers. Additionally, we propose a simple solution to the problem of data shrinkage produced by the linear local fitting of the principal component analysis. The proposed method is simple, easy to implement, and effective for noise filtering.

References

  1. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., and Silva, C.T., 2001. Point set surfaces. In Proceedings of the Conference on Visualization, pages 21-28. IEEE Computer Society.
  2. Bajaj, C., L., and XU, G. 2003. Anisotropic diffusion of subdivision surfaces and functions on surfaces. ACM Transactions on Graphics (TOG) 22, 1, 4-32.
  3. Choudhury, P., and Tumblin, J., 2003. The Trilateral Filter for High Contrast Images and Meshes. Eurographics Symposium on Rendering, pp. 1.11
  4. De la Torre, F., and Black, M.J., 2001. Robust principal component analysis for computer vision. In ICCV'01, I: 362-369.
  5. Desbrun, M., Meyer, M., Schroder, P., and Barr, A. H. 1999. Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow. In Proceedings of SIGGRAPH, 317-324.
  6. Desbrun, M., Meyer, M., Schroder, P., and Barr, A. H. 2000. Anisotropic Feature-Preserving Denoising of Height fields and Bivariate Data. In Graphics Interface, 145-152.
  7. Fleishman, S., Drori, I., and Cohen-Or, D., 2003. Bilateral mesh denoising. ACM Transactions on Graphics (TOG), 22(3):950-953.
  8. Gumhold, S., Wang, X., and MacLeod, R., 2001. Feature extraction from point clouds. In 10th International Meshing Roundtable, Sandia National Laboratories, pages 293-305, October.
  9. Huber, P. J., 1981. Robust Statistics. John Wiley and Sons.
  10. Hubert, M., Rousseuw, P.J., and Branden, K.V., 2005. ROBPCA: A New Approach to Robust Principal Component. Analysis.Technometrics, February, VOL. 47, NO. 1.
  11. Jolliffe, I., 1986. Principal Component Analysis. New York:Springer-Verlag.
  12. Jones, T. R., Durand, F., and Desbrun, M., 2003. Noniterative, feature-preserving mesh smoothing. ACM Transactions on Graphics (TOG), 22(3):943-949.
  13. Martinez, W.L., and Martinez, A.R., 2002. Computational statistics handbook with Matlab. Chapman & Hall/CRC.
  14. Mederos, B., Velho L., and De Figueiredo L. H., 2003. Robust smoothing of noisy point clouds. In Proc. SIAM Conference on Geometric Design and Computing (Seattle, USA), Nashboro Press.
  15. Pauly, M., Gross, M., and Kobbelt, L., 2002. Efficient simplification of point-sampled surfaces. IEEE Vizualization, pp. 163-170.
  16. Pauly, M., and M. Gross., 2001. Spectral processing of point-sampled geometry. Proc. ACM SIGGRAPH, pp. 279-386.
  17. Peng, J., Strela, V., and Zorin, D. 2001. A Simple Algorithm for Surface Denoising. In Proceedings of IEEE Visualization, 107-112.
  18. Rousseeuw, P. J., and Driessen, K.V., 1999. A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics, 41, 212-223.
  19. Skocal, D., and Leonardis, A., 2002. Weighted Incremental Subspace Learning. Proceedings of Workshop on Cognitive Vision. Zurich, Sep.
  20. Schall, O., Belyaev, A., and Seidel, H., 2005. Robust Filtering of Noisy Scattered Point Data. Eurographics Symposium on Point-Based Graphics.
  21. Taubin, G., 1995. A Signal Processing Approach to Fair Surface Design. In Proceedings of SIGGRAPH, 351- 358.
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Paper Citation


in Harvard Style

A. Leal Narváez E. and Eduardo Leal Narváez N. (2006). POINT CLOUD DENOISING USING ROBUST PRINCIPAL COMPONENT ANALYSIS . In Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, ISBN 972-8865-39-2, pages 51-58. DOI: 10.5220/0001358900510058


in Bibtex Style

@conference{grapp06,
author={Esmeide A. Leal Narváez and Nallig Eduardo Leal Narváez},
title={POINT CLOUD DENOISING USING ROBUST PRINCIPAL COMPONENT ANALYSIS},
booktitle={Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,},
year={2006},
pages={51-58},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001358900510058},
isbn={972-8865-39-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,
TI - POINT CLOUD DENOISING USING ROBUST PRINCIPAL COMPONENT ANALYSIS
SN - 972-8865-39-2
AU - A. Leal Narváez E.
AU - Eduardo Leal Narváez N.
PY - 2006
SP - 51
EP - 58
DO - 10.5220/0001358900510058