Journal of the Korea Computer Graphics Society (한국컴퓨터그래픽스학회논문지)

Korea Computer Graphics Society (한국컴퓨터그래픽스학회)
권호 표지
DOI QR코드

DOI QR Code

Surface Reconstruction from Oriented Point Cloud Using a Box-Spline on the BCC Lattice

BCC 격자의 박스-스플라인을 이용한 입체 표면 복구 기법

  • Kim, Hyunjun (Institute of Industrial Technology, University of Seoul) ;
  • Kim, Minho (Department of Computer Science and Engineering, University of Seoul)
  • 김현준 (서울시립대학교 부설 산업기술 연구소) ;
  • 김민호 (서울시립대학교 컴퓨터과학부)
  • Received : 2015.03.31
  • Accepted : 2015.05.09
  • Published : 2015.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose an improved surface reconstruction method from an oriented point cloud. Our method is a classical least-square scheme, but is based on the 7-direction box-spline and the BCC (Body-Centered Cubic) lattice, which results in surfaces with superior quality and lower computational overhead, compared to other methods based on the B-splines on the Cartesian lattice. Specifically, when compared with two of the most popular techniques our method results in better surfaces but only takes ${\approx}53%$ computation time.

본 논문에서는 방향성이 있는 포인트 클라우드로부터 3차원 개체의 표면을 복구하는 향상된 기법을 제안한다. 본 방법은 기존에 널리 사용되고 있는 최소 자승법에 기초하고 있지만, 7-방향 박스-스플라인과 체심입방(BCC: Body-Centered)격자를 활용하여 카티시안 격자와 B-스플라인에 기반한 기존의 방법들에 비해 좀 더 나은 품질의 곡면을 빠른 시간에 얻을 수 있다. 구체적으로는, 기존의 두 방법론과 비교해 보았을 때 본 방법은 평균적으로 약 53%의 연산시간만에 좀 더 나은 품질의 곡면을 얻을 수 있다.

Keywords

References

  1. M. Kim, "Quartic box-spline reconstruction on the BCC lattice," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 2, pp. 319-330, Feb. 2013. https://doi.org/10.1109/TVCG.2012.130
  2. D. P. Petersen and D. Middleton, "Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces," Information and Control, vol. 5, no. 4, pp. 279-323, 1962. https://doi.org/10.1016/S0019-9958(62)90633-2
  3. M. Kazhdan, M. Bolitho, and H. Hoppe, "Poisson surface reconstruction," in Proceedings of the Fourth Eurographics Symposium on Geometry Processing, ser. SGP '06. Aire-la-Ville, Switzerland, Switzerland: Eurographics Association, 2006, pp. 61-70.
  4. F. Calakli and G. Taubin, "SSD: Smooth signed distance surface reconstruction," Computer Graphics Forum, vol. 30, no. 7, pp. 1993-2002, 2011. https://doi.org/10.1111/j.1467-8659.2011.02058.x
  5. M. Kazhdan and H. Hoppe, "Screened Poisson surface reconstruction," ACM Trans. Graph., vol. 32, no. 3, pp. 29:1-29:13, July 2013.
  6. B. Juttler and A. Felis, "Least-squares fitting of algebraic spline surfaces," Advances in Computational Mathematics, vol. 17, no. 1-2, pp. 135-152, 2002. https://doi.org/10.1023/A:1015200504295
  7. A. Entezari, R. Dyer, and T. Moller, "Linear and cubic box splines for the body centered cubic lattice," in IEEE Visualization. IEEE Computer Society, 2004, pp. 11-18.
  8. B. Csebfalvi and M. Hadwiger, "Prefiltered B-spline reconstruction for hardware-accelerated rendering of optimally sampled volumetric data," in Vision, Modeling, and Visualization, 2006, pp. 325-332.
  9. C. de Boor, K. Hollig, and S. Riemenschneider, Box splines. Springer-Verlag New York, Inc., 1993.
  10. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed. New York, NY, USA: Springer-Verlag New York, Inc., 1998.
  11. M. Kim and J. Peters, "Symmetric box-splines on root lattices," Journal of Computational and Applied Mathematics, vol. 235, no. 14, pp. 3972-3989, May 2011. https://doi.org/10.1016/j.cam.2010.11.027
  12. M. Kim, H. Kim, and A. Sarfaraz, "Efficient gpu isosurface raycasting of BCC datasets," Journal of the Korea Computer Graphics Society, vol. 19, no. 2, pp. 19-27, June 2013. https://doi.org/10.15701/kcgs.2013.19.2.19
  13. E. Kreyszig, Introductory Functional Analysis With Applications, ser.Wiley Classics Library. JohnWiley & Sons, 1978.
  14. SSI (Scalable Software Infrastructure for Scientific Computing), "LIS (library for iterative solvers for linear systems)," http://www.ssisc.org/lis, accessed: 2014-10-8.
  15. M. Berger, J. A. Levine, L. G. Nonato, G. Taubin, and C. T. Silva, "A benchmark for surface reconstruction," ACM Trans. Graph., vol. 32, no. 2, pp. 20:1-20:17, Apr. 2013.

Cited by

  1. Compactly Supported Biorthogonal Wavelet Bases on the Body Centered Cubic Lattice vol.36, pp.3, 2015, https://doi.org/10.1111/cgf.13166