Browse > Article
http://dx.doi.org/10.12941/jksiam.2019.23.031

AN EXPLICIT NUMERICAL ALGORITHM FOR SURFACE RECONSTRUCTION FROM UNORGANIZED POINTS USING GAUSSIAN FILTER  

KIM, HYUNDONG (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
LEE, CHAEYOUNG (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
LEE, JAEHYUN (SEOUL SCIENCE HIGH SCHOOL)
KIM, JAEYEON (SEOUL SCIENCE HIGH SCHOOL)
YU, TAEYOUNG (SEOUL SCIENCE HIGH SCHOOL)
CHUNG, GENE (SEOUL SCIENCE HIGH SCHOOL)
KIM, JUNSEOK (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.23, no.1, 2019 , pp. 31-38 More about this Journal
Abstract
We present an explicit numerical algorithm for surface reconstruction from unorganized points using the Gaussian filter. We construct a surface from unorganized points and solve the modified heat equation coupled with a fidelity term which keeps the given points. We apply the operator splitting method. First, instead of solving the diffusion term, we use the Gaussian filter which has the effect of diffusion. Next, we solve the fidelity term by using the fully implicit scheme. To investigate the proposed algorithm, we perform computational experiments and observe good results.
Keywords
Unorganized points; surface reconstruction; operator splitting method; Gaussian filter;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. Taubin, Curve and surface smoothing without shrinkage, In Proceedings of IEEE international conference on Computer Vision, (1995), 852-857.
2 T. Bulow, Spherical diffusion for 3D surface smoothing, IEEE Trans. Pattern Anal. Mach. Intell. 26, (2004), 1650-1654.   DOI
3 T. Tasdizen, R. Whitaker, P. Burchard, and S. Osher, Geometric surface smoothing via anisotropic diffusion of normals, In Proceedings of the conference on Visualization, (2002), 125-132.
4 T. R. Jones, F. Durand, and M. Desbrun, Non-iterative, feature-preserving mesh smoothing, ACM Trans. Graphics 22 (2003), 943-949.   DOI
5 L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D. 60 (1992), 259-268.   DOI
6 L. Vese, and S. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, J. Sci. Comput. 19 (2003), 553-572.   DOI
7 H. K. Zhao, S. Osher, and R. Fedkiw, Fast surface reconstruction using the level set method, In Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, (2001), 194-201.
8 Y. Li, D. Lee, C. Lee, J. Lee, S. Lee, J. Kim, S. Ahn, and J. Kim, Surface embedding narrow volume reconstruction from unorganized points, Comput. Vis. Image Underst. 121 (2014), 100-107.   DOI
9 Y. Li and J. Kim, Fast and efficient narrow volume reconstruction from scattered data, Pattern Recognit. 48 (2015), 4057-4069.   DOI
10 D. Jeong, Y. Li, H. Lee, S. Lee, J. Yang, S. Park, H. Kim, Y. Choi, and J. Kim, Efficient 3D volume reconstruction from a point cloud using a phase-field method, Math. Probl. Eng. (2018).
11 L. Rudin, and S. Osher, Total variation based image restoration with free local constraints, In Proceedings of 1st International Conference on Image Processing, 1 (1994), 31-35.
12 Stanford university computer graphics laboratory, http://lightfield. stanford.edu/acq.html.
13 H. Li, Y. Li, R. Yu, J. Sun, and J. Kim, Surface reconstruction from unorganized points with $l_0$ gradient minimization, Comput. Vis. Image Underst. 169 (2018) 108-118.   DOI
14 Y. Li and J. Kim, A fast and accurate numerical method for medical image segmentation, J. KSIAM. 14 (2010), 201-210.