Abstract
We consider the problem of approximating normal and feature sizes of a surface from point cloud data that may be noisy. These problems are central to many applications dealing with point cloud data. In the noise-free case, the normals and feature sizes can be approximated by the centers of a set of unique large Delaunay balls called polar balls. In presence of noise, polar balls do not necessarily remain large and hence their centers may not be good for normal and feature size approximations. Earlier works suggest that some large Delaunay balls can play the role of polar balls. However, these results were short in explaining how the big Delaunay balls should be chosen for reliable approximations and how the approximation error depends on various factors. We provide new analyses that fill these gaps. In particular, they lead to new algorithms for practical and reliable normal and feature approximations.
This work is partially supported by NSF CARGO grant DMS-0310642 and ARO grant DAAD19-02-1-0347.
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References
Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.: Point set surfaces. In: Proc. IEEE Visualization, pp. 21–28 (2001)
Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. Discr. Comput. Geom. 22, 481–504 (1999)
Amenta, N., Bern, M., Eppstein, D.: The crust and the β-skeleton: combinatorial curve reconstruction. Graphical Models and Image Processing 60, 125–135 (1998)
Amenta, N., Choi, S., Kolluri, R.K.: The power crust, union of balls, and the medial axis transform. Comput. Geom.: Theory Applications 19, 127–153 (2001)
Attali, D., Montanvert, A.: Modeling noise for a better simplification of skeletons. In: Proc. Internat. Conf. Image Process., vol. 3, pp. 13–16 (1996)
Boissonnat, J.D., Cazals, F.: Natural neighbour coordinates of points on a surface. Comput. Geom. Theory Applications, 87–120 (2001)
Chazal, F., Lieutier, A.: Stability and homotopy of a subset of the medial axis. In: Proc. ACM Sympos. Solid Modeling and Applications, pp. 243–248 (2004)
Dey, T.K., Goswami, S.: Provable surface reconstruction from noisy samples. In: Proc. 20th Annu. Sympos. Comput. Geom., pp. 330–339 (2004)
Dey, T.K., Sun, J.: Adaptive MLS surfaces for reconstruction with guarantees. In: Proc. Eurographics Sympos. Geom. Processing, pp. 43–52 (2005)
Dey, T.K., Zhao, W.: Approximating the medial axis from the Voronoi diagram with a convergence guarantee. Algorithmica 38, 179–200 (2003)
Kolluri, R.: Provably good moving least squares. In: Proc. ACM-SIAM Sympos. Discrete Algorithms, pp. 1008–1017 (2005)
Mederos, B., Amenta, N., Velho, L., de Figueiredo, H.: Surface reconstruction from noisy point clouds. In: Proc. Eurographics Sympos. Geom. Processing, pp. 53–62 (2005)
Mitra, N., Nguyen, J., Guibas, L.: Estimating surface normals in noisy point cloud data. Internat. J. Comput. Geom. & Applications (2004)
Pauly, M., Keiser, R., Kobbelt, L., Gross, M.: Shape modeling with point-sampled geometry. In: Proc. ACM SIGGRAPH 2003, pp. 641–650 (2003)
Dey, T.K., Sun, J.: Normal and Feature Approximations from Noisy Point Clouds. Technical Report OSU-CISRC-4-05-TR26 (2005)
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Dey, T.K., Sun, J. (2006). Normal and Feature Approximations from Noisy Point Clouds. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_5
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DOI: https://doi.org/10.1007/11944836_5
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