Journal of Korea Multimedia Society (한국멀티미디어학회논문지)

Korea Multimedia Society (한국멀티미디어학회)
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Feature Extraction Algorithm from Polygonal Model using Implicit Surface Fitting

음함수 곡면 맞춤을 이용한 다각형 모델로부터 특징 추출 알고리즘

  • 김수균 (배재대학교 게임공학과)
  • Published : 2009.01.30
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Abstract

This paper proposes a extraction of feature lines on a polygonal model using local implicit surface fitting technique. To extract feature lines on a polygonal model, the previous technique addressed to compute the curvature and their derivatives at mesh vertices via global implicit surface fitting. It needs a user-specified precision parameter for finding an accurate projection of the mesh vertices onto an approximating implicit surface and requires high-time consumption. But we use a local implicit surface fitting technique to estimate the local differential information near a vertex by means of an approximating surface. Feature vertices are easily detected as zero-crossings, and can then be connected along the direction of principal curvature. Our method, demonstrated on several large polygonal models, produces a good fit which leads to improved visualization.

본 논문은 3차원 다각형 모델에서 특징 선을 추출하기 위한 방법에 대해 제안한다. 이산 곡면으로 이루어진 다각형 모델에서 특징 선을 추출하기 위하여 기존 방법에서는 전역적인 음함수 곡면 맞춤 기법(Implicit Surface Fitting)을 이용하여 모델의 꼭지점에서 곡률과 곡률 미분 값을 측정하였다. 이러한 방법은 다각형 모델의 꼭지점에서 음함수 곡면으로 정확하게 투영할 수 있도록 사용자의 정의 파라미타를 찾아야 하며, 특징 추출을 위한 많은 계산 시간을 요구한다. 그러나 제안 방법은 지역적 음함수 곡면 맞춤 기법을 이용하여 모델의 꼭지점에 근사된 곡면을 통해 미분 정보를 측정한다. 측정된 미분 정보를 통해 쉽게 각각의 모서리에서 제로-클로싱을 통해 특징 점을 추출하고, 곡률 방향을 따라 추출된 점들을 연결하여 특징 선을 생성한다. 여러 가지 다각형 모델에서 실험을 하였고 기존 방법보다 빠르며 높은 품질의 특징 선을 추출한다.

Keywords

References

  1. P. Alliez, M. Meyer, and M. Desbrun, "Interactive geometry remeshing," Proceedings of SIGGRAPH, pp. 347-354, 2002.
  2. G.G. Gorden, "Face recognition based on depth maps and surface curvature," Proceedings of the SPIE: Geometric Methods in Computer Vision, pp. 234-247, 1991.
  3. P.L. Hallinan, G.G. Gordon, A.L. Yuille, P. Giblin, and D. Mumford, Two-and-Three Dimensional Patterns of the Face, A. K. Peters Publishers, 1999.
  4. A. Hubeli and M. Gross, "Multiresolution feature extraction from unstructured meshes," Proceedings of IEEE Visualization 2001, pp. 287-294, 2001.
  5. J.T. Kent, K.V. Mardia and J. West, "Ridge curves and shape analysis," Proceedings of the British Machine Vision Conference 1996, pp. 43-52, 1996.
  6. J. Vorsatz, C. RossI, L.P. Kobbelt and H.-P. Seidel, "Feature sensitive remeshing," Computer Graphics Forum, Vol.20, No.3, pp. 393-401, 2001. https://doi.org/10.1111/1467-8659.00532
  7. K. Watanabe and A.G. Belyaev, "Detection of salient curvature features on polygonal surfaces," Computer Graphics Forum, Vol.20, No.3, pp. 385-392, 2001. https://doi.org/10.1111/1467-8659.00531
  8. O. Monga, S. Benayoun and O. Faugerras, "From partial derivatives of 3D density images to ridge lines," Proceedings of CVPR, pp. 354-359, 1992.
  9. O. Monga, N. Armande and P. Montesionoss, "Thin nets and crest lines: application to satellite data and medical images," Computer Vision and Image Understanding archive, Vol.67, Issue 3, pp. 285-295, 1997. https://doi.org/10.1006/cviu.1996.0507
  10. X. Pennec, N. Ayache and J.P. Thirion, Landmark-based registration using features identified through differential geometry, Handbook of Medical Imaging, I. N. Bankman, ed. Academic Press, pp. 499-513, 2000.
  11. F. Cazals, and M. Pouget, "Estimating differential quantities using polynomial fitting of osculating jets," Proceedings of a Symposium on Geometry Processing, pp. 177-187, 2003.
  12. J. Goldfeather and V. Interrante, "A novel cu-bie-order algorithm for approximating principal direction vectors," ACM Transaction on Graphics, Vol.23, No.1, pp. 45-63, 2004. https://doi.org/10.1145/966131.966134
  13. D.L. Page, Y. Sun, A. Koschan, J. Paik and M. Abidi, "Normal vector voting: crease detection and curvature estimation on large, noisy meshes," Graphical Models, Vol.64, Issue 3/4, pp.199-229, 2002. https://doi.org/10.1006/gmod.2002.0574
  14. C. Rossl, L. Kobbelt and H.-P. Seidel, "Extraction of feature lines on triangulated surfaces using morphological operators. Smart Graphics," Proceedings of the AAAI Spring Symposium, pp. 71-75, 2000.
  15. G. Stylianou and G. Falin, "Crest Jines extraction from 3D triangulated meshes. Hierarchical and Geometrical Methods in Scientific Visualization,' Springer, G. Farin, E. Hamann, and H. Hagen, eds., pp. 269-281, 2003.
  16. Y. Ohtake, A.G. Belyaev and H.-P. Seidel, "Ridge valley lines on meshes via implicit surface fitting," Proceedings of SIGGRAPH, pp. 609-612, 2004.
  17. S. Yoshizawa, A.G. Belyaev and H.-P. Seidel, "Fast and robust detection of crest lines on meshes," Proceedings of the ACM symposium on solid and physical modeling. pp. 227-232, 2005.
  18. D. Levin, G. Brunnett, B. Hamann, H. Muller and L. Linsen, "Mesh-independent surface interpolation," Geometric Modeling for Scientific Visualization 2004, Springer-Verlag, pp. 3750, 2004.
  19. J.P. Thirion, "The extremal mesh and understanding of 3D surfaces," INRIA Research Report 2149, Dec. 1993.
  20. N. Dyn, K. Hormann, S.-J. Kim, and D. Levin, "Optimizing 3D triangulations using discrete curvature analysis," Mathematical Methods for Curves and Surface, pp. 135-146, 2001.
  21. Y. Ohtake, A.G. Belyaev and H.-P. Seidel, "A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions," Proceedings of Shape Modeling International, pp. 153-161, 2003.
  22. S. Gumhold, X. Wang and M.I. Miller, "Feature extraction from point clouds," Proceedings of the 10th International Meshing Roundtable, pp. 293-305, 2001.
  23. M. Pauly, R. Keiser and M. Gross, "Multi-scale feature extraction on point-sampled models," Computer Graphics Forum, Vol.22, Issue 3, pp. 281-289, 2003. https://doi.org/10.1111/1467-8659.00675