Feature-preserving non-local denoising of static and time-varying range data

ABSTRACT

We present a new method for noise removal on static and time-varying range data. Our approach predicts the restored position of a perturbed vertex using similar vertices in its neighborhood. It defines the required similarity measure in a new non-local fashion which compares regions of the surface instead of point pairs. This allows our algorithm to obtain a more accurate denoising result than previous state-of-the-art approaches and, at the same time, to better preserve fine features of the surface. Furthermore, our approach is easy to implement, effective, and flexibly applicable to different types of scanned data. We demonstrate this on several static and interesting new time-varying datasets obtained using laser and structured light scanners.

References

1. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., and Silva, C. T. 2001. Point set surfaces. IEEE Visualization 2001 (Oct.), 21--28.
2. Alexa, M. 2002. Wiener filtering of meshes. In Proceedings of Shape Modeling International, 51--57.
3. Amenta, N., and Kil, Y. J. 2004. Defining point-set surfaces. ACM Transactions on Graphics 23, 3 (August), 264--270. Proceedings of SIGGRAPH 2004.
4. Awate, S. P., and Whitaker, R. T. 2006. Unsupervised, information-theoretic, adaptive image filtering with applications to image restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) 28, 3 (March), 364--376.
5. Bennett, E. P., and McMillan, L. 2005. Video enhancement using per-pixel virtual exposures. ACM Transactions on Graphics 24, 3, 845--852. Proceedings of ACM SIGGRAPH 2005.
6. Buades, A., Coll, B., and Morel, J. M. 2005. A non-local algorithm for image denoising. In Computer Vision and Pattern Recognition (CVPR) 2005, vol. 2, 60--65.
7. Davis, J., Nehab, D., Ramamoothi, R., and Rusinkiewicz, S. 2005. Spacetime stereo: A unifying framework for depth from triangulation. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) 27, 2 (February), 296--302.
8. Desbrun, M., Meyer, M., Schröder, P., and Barr, A. H. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proceedings of SIGGRAPH 99, 317--324.
9. Dey, T. K., and Sun, J. 2005. Adaptive MLS surfaces for reconstruction with guarantees. In Eurographics Symposium on Geometry Processing 2005, 43--52.
10. Efros, A. A., and Leung, T. K. 1999. Texture synthesis by non-parametric sampling. In International Conference on Computer Vision (ICCV'99), Volume 2, 1033--1038.
11. Fleishman, S., Drori, I., and Cohen-Or, D. 2003. Bilateral mesh denoising. ACM Transactions on Graphics 22, 3, 950--953. Proceedings of ACM SIGGRAPH 2003.
12. Fleishman, S., Cohen-Or, D., and Silva, C. T. 2005. Robust moving least-squares fitting with sharp features. ACM Transactions on Graphics 24, 3, 544--552. Proceedings of ACM SIGGRAPH 2005.
13. Hildebrandt, K., and Polthier, K. 2004. Anisotropic filtering of non-linear surface features. Computer Graphics Forum 23, 3, 391--400. Proceedings of EUROGRAPHICS 2004.
14. Jenke, P., Wand, M., Bokeloh, M., Schilling, A., and Strasser, W. 2006. Bayesian point cloud reconstruction. Computer Graphics Forum 25, 3. Proceedings of EUROGRAPHICS 2006.
15. Jones, T. R., Durand, F., and Desbrun, M. 2003. Non-iterative feature-preserving mesh smoothing. ACM Transactions on Graphics 22, 3 (July), 943--949. Proceedings of SIGGRAPH 2003.
16. Lange, C., and Polthier, K. 2005. Anisotropic fairing of point sets. Special Issue of Computer Aided Geometric Design 22, 7, 680--692.
17. Levin, D. 1998. The approximation power of moving least-squares. Math. Comput. 67, 224, 1517--1531.
18. Mahmoudi, M., and Sapiro, G. 2005. Fast image and video denoising via nonlocal means of similar neighborhoods. Signal Processing Letters 12, 12, 839--842.
19. 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, Nashboro Press, Seattle, USA.
20. Paris, S., and Durand, F. 2006. A fast approximation of the bilateral filter using a signal processing approach. In European Conference on Computer Vision (ECCV).
21. Pauly, M., and Gross, M. 2001. Spectral processing of point-sampled geometry. Proceedings of SIGGRAPH 2001, 379--386.
22. Pauly, M., Mitra, N. J., and Guibas, L. J. 2004. Uncertainty and variability in point cloud surface data. In Eurographics Symposium on Point-Based Graphics, 77--84.
23. Perona, P., and Malik, J. 1990. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 7, 629--639.
24. Rudin, L. I., Osher, S., and Fatemi, E. 1992. Nonlinear total variation based noise removal algorithms. In Physica D 60, Elsevier North-Holland, Inc., 259--268.
25. Schall, O., Belyaev, A. G., and Seidel, H.-P. 2005. Robust filtering of noisy scattered point data. In Eurographics Symposium on Point-Based Graphics 2005, M. Pauly and M. Zwicker, Eds., 71--77.
26. Sharf, A., Alexa, M., and Cohen-Or, D. 2004. Context-based surface completion. ACM Transactions on Graphics 23, 3 (August), 878--887. Proceedings of SIGGRAPH 2004.
27. Tasdizen, T., Whitaker, R., Burchard, P., and Osher, S. 2002. Geometric surface smoothing via anisotropic diffusion of normals. In Proceedings of IEEE Visualization 2002, IEEE Computer Society, Washington, DC, USA, 125--132.
28. Taubin, G. 1995. A signal processing approach to fair surface design. In Proceedings of SIGGRAPH 95, 351--358.
29. Tomasi, C., and Manduchi, R. 1998. Bilateral filtering for gray and color images. In Proceedings of the Sixth International Conference on Computer Vision (ICCV), 839--846.
30. Wei, L.-Y., and Levoy, M. 2000. Fast texture synthesis using tree-structured vector quantization. In Proceedings of ACM SIGGRAPH 2000, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 479--488.
31. Yaroslavsky, L. P. 1985. Digital Picture Processing. An Introduction. Springer Verlag, Berlin, Heidelberg.
32. Yoshizawa, S., Belyaev, A., and Seidel, H.-P. 2006. Smoothing by example: Mesh denoising by averaging with similarity-based weights. In Proceedings of Shape Modeling International, 38--44.
33. Zhang, L., Snavely, N., Curless, B., and Seitz, S. M. 2004. Spacetime faces: High resolution capture for modeling and animation. ACM Transactions on Graphics 23, 3, 548--558. Proceedings of SIGGRAPH 2004.

Index Terms

• Applied computing

  • Arts and humanities

    • Architecture (buildings)

      • Computer-aided design

  • Physical sciences and engineering

    • Engineering

      • Computer-aided design

• Computing methodologies

  • Computer graphics

    • Shape modeling

      • Parametric curve and surface models

      • Volumetric models