Journal of KIISE:Computing Practices and Letters (한국정보과학회논문지:컴퓨팅의 실제 및 레터)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Point Set Denoising Using a Variational Bayesian Method

변분 베이지안 방법을 이용한 점집합의 오차제거

  • 윤민철 (포항공과대학교 컴퓨터공학과) ;
  • ;
  • 이승용 (포항공과대학교 컴퓨터공학과)
  • Published : 2008.07.15
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Abstract

For statistical modeling, the model parameters are usually estimated by maximizing a probability measure, such as the likelihood or the posterior. In contrast, a variational Bayesian method treats the parameters of a model as probability distributions and computes optimal distributions for them rather than values. It has been shown that this approach effectively avoids the overfitting problem, which is common with other parameter optimization methods. This paper applies a variational Bayesian technique to surface fitting for height field data. Then, we propose point cloud denoising based on the basic surface fitting technique. Validation experiments and further tests with scan data verify the robustness of the proposed method.

스캐너를 이용해 스캔한 데이타는 오차를 포함하고 있으며, 이러한 오차는 통계적인 성질을 갖는 경우가 많다. 이러한 이유에서 통계적인 방법은 오차 처리를 위해 매우 효과적인 방법이며, 최근 많은 연구가 이루어지고 있다. 이러한 통계적인 방법 중 대표적인 방법인 점 추정 방법은 데이타의 여러 성질을 나타내지 못하고 단지 확률이 최대가 되는 부분의 성질만을 나타내는 한계가 있으며, 이러한 한계로 인하여 오버피팅 문제가 발생하게 된다. 이러한 한계를 극복하고 오버피팅 문제를 해결하기 위해서 본 논문에서는 변분 베이지안 방법을 이용한다. 점집합의 오차를 제거하기 위해 지역적 근사곡면을 사용하고, 높이함수를 이용해서 근사곡면을 나타낸다. 변분 베이지안 방법을 사용하여 오차가 제거된 근사곡면을 구하고, 주어진 점들을 근사곡면으로 매핑하여 오차를 제거한다. 제시된 방법은 계량적 실험과 실제 스캔된 자료를 이용한 실험을 통하여 검증된다.

Keywords

References

  1. Miskin, J. W. Ensemble Learning for Independent Component Analysis. PhD thesis, Department of Physics, University of Cambridge, 2001
  2. Taubin, G. "A signal processing approach to fair surface design," In Proc. of SIGGRAPH 95, pp 351-358, 1995
  3. Mederos, B., Velho, L., and Figueiredo, L. "Robust smoothing of noisy point clouds," In Proc. of SIAM Conference on Geometric Design and Computing, Seattle 2003, 2004
  4. Pauly, M., Mitra, N. J., and Guibas, L. "Uncertainty and variability in point cloud surface data," In Proc. of Symposium on Point-Based Graphics, pp. 77-84, 2004
  5. Kalaiah, A., and Varshney, A. "Statistical geometry representation for efficient transmission and rendering," ACM Transactions on Graphics, Vol. 24, No. 2, pp. 348-373, 2005 https://doi.org/10.1145/1061347.1061356
  6. Sorenson, H. W. "Least-squares estimation: From Gauss to Kalman," IEEE Spectrum, Vol. 7, pp. 63-68, 1970
  7. Steinke, F., Scholkopf, B., and Blanz, V. "Support vector machines for 3D shape processing," Computer Graphics Forum Vol. 24, No. 3, pp 285-294, 2005 https://doi.org/10.1111/j.1467-8659.2005.00853.x
  8. Diebel, J. R., Thrun, S., and Brunig, M. "A Bayesian method for probable surface reconstruction and decimation," ACM Transactions on Graphics, Vol. 25, No. 1, pp. 39-59, 2006 https://doi.org/10.1145/1122501.1122504
  9. Jenke, P., Wand, M., Bokeloh, M., Schilling, A., and Strasser. W. "Bayesian point cloud reconstruction," Computer Graphics Forum, Vol. 25, No. 3, pp. 379-388, 2006 https://doi.org/10.1111/j.1467-8659.2006.00957.x
  10. Miskin, J. W., and MacKay, D. J. C. "Ensemble learning for blind image separation and deconvolution," In M. Girolami, editor, Advances in Independent Component Analysis. Springer-Verlag, 2000
  11. Fergus, R., Singh, B., Hertzmann, A., Roweis, S. T., and Freeman. W. T. "Removing camera shake from a single photograph," ACM Transactions on Graphics, Vol. 25, No. 3, pp. 787-794, 2006 https://doi.org/10.1145/1141911.1141956
  12. Cignoni, P., Rocchini, C., and Scopigno, R. "Metro: Measuring error on simplified surfaces," Computer Graphics Forum, Vol. 17, No 2. pp. 167-174, 1998 https://doi.org/10.1111/1467-8659.00236
  13. Ohtake, Y., Belyaev, A., and Seidel, H. -P. "3d scattered data approximation with adaptive compactly supported radial basis functions," In Proc. of Shape Modeling International," pp. 31-39. IEEE, 2004
  14. Dey, T. K., and Goswami, S. "Tight cocone: a water-tight surface reconstructor," In Proc. of Symposium on Solid Modeling and Applications, pp. 127-134, 2003