Journal of the Korea Computer Graphics Society (한국컴퓨터그래픽스학회논문지)

Korea Computer Graphics Society (한국컴퓨터그래픽스학회)
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Geometry Reconstruction Using Dictionary Learning of 3D Shape Features

3차원 형태 특징의 사전 학습을 이용한 기하 복원

  • Hwang, Jung-Min (Department of Computer Engineering, Sejong University) ;
  • Yoon, Yeo-Jin (Department of Computer Engineering, Sejong University) ;
  • Choi, Soo-Mi (Department of Computer Engineering, Sejong University)
  • 황정민 (세종대학교 컴퓨터공학과) ;
  • 윤여진 (세종대학교 컴퓨터공학과) ;
  • 최수미 (세종대학교 컴퓨터공학과)
  • Received : 2017.02.10
  • Accepted : 2017.03.07
  • Published : 2017.03.07
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Abstract

In this paper, we present a dictionary learning method for reducing errors in point cloud models and reconstructing their geometry. For this, 3D feature information is extracted from the models which have a similar shape characteristic as the target model. Then a dictionary is constructed and the geometry is reconstructed using the dictionary. The presented method in this paper consists of the following three steps. First, a geometric patch is constructed from a similar model. Second, a morphological 3D feature of the acquired patch is learned. Third, a geometry reconstruction is performed using the learned dictionary. Finally, the error between the original model and the reconstruction result is calculated, and the accuracy of the reconstruction result is checked.

본 논문에서는 포인트 클라우드로 구성된 모델 내의 오류를 줄이고, 기하학적 형태를 복원하기 위한 사전 학습 방법을 제시한다. 이를 위해, 대상 모델과 유사한 형태 특징을 갖는 모델로부터 3차원 특징 정보를 추출하여 사전을 구성하고, 이를 통해 기하 복원을 수행한다. 본 연구에서 제시한 방법은 다음과 같이 세 단계로 구성된다. 첫째, 유사 모델로부터 기하 패치를 구성하는 단계, 둘째, 획득한 패치의 3차원 형태 특징을 학습하는 단계, 셋째, 학습된 사전을 이용하여 기하를 복원하는 단계이며, 최종적으로 원본 모델과 복원 결과의 오차를 계산하며, 복원 결과의 정확도를 확인한다.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira. M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J.Shade and D. Fulk, s"The Digital Michelangelo Project: 3D Scanning of Large Statues", In Proc. ACM SIGGRAPH, pp. 131-144, 2000.
  2. D. Levin, "Mesh-Independent Surface Interpolation", Geometric modeling for scientific visualization, pp. 37-49, 2001.
  3. J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum and T. R. Evans, "Reconstruction and Representation of 3D Objects with Radial Basis Functions", In Proc. ACM SIGGRAPH, pp. 67-76, 2001.
  4. R. Kolluri, J. R. Shewchuk and J. F. O'Brien, "Spectral Surface Reconstruction from Noisy Point Clouds", In Proc. Symposium on Computational geometry, pp. 11-21, 2004.
  5. J. Digne, J. M. Morel, C. M. Souzani and C. Lartigue, "Scale Space Meshing of Raw Data Point Sets", Computer Graphics Forum, 30(6): 1630-1642, 2011. https://doi.org/10.1111/j.1467-8659.2011.01848.x
  6. W. E. Lorensen and H. E. Cline, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm", In Proc. ACM SIGGRAPH, 21(4): 163-169, 1987.
  7. M. Kazhdan, M. Bolitho and H. Hoppe, "Poisson Surface Reconstruction", In Proc. Symposium on Geometry Processing, pp. 61-70, 2006.
  8. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald and W. Stuetzle, "Surface Reconstruction from Unorganized Points", In Proc. ACM SIGGRAPH, 26(2): 71-78, 1992.
  9. G. Guennebaud and M. Gross, "Algebraic Point Set Surfaces", ACM Transactions on Graphics, 26(3): 23:1-23:9, 2007.
  10. E. Candes, J. Romberg and T. Tao, "Stable Signal Recovery from Incomplete and Inaccurate Measurements", Communications on Pure and Applied Mathematics, 59(8): 1207-1223, 2006. https://doi.org/10.1002/cpa.20124
  11. D. Ge, X. Jiang and Y. Ye, "A Note on the Complexity of $L_1$ Minimization", Mathematical Programming, 129(2): 285-299, 2011. https://doi.org/10.1007/s10107-011-0470-2
  12. E. Candes and J. Romberg, "$\ell_1$-MAGIC : Recovery of Sparse Signals via Convex Programming", Technical Report, Caltech. Pasadena, Califonia, 2005.
  13. Y. Sharon, J. Wright and Y. Ma, "Computation and relaxation of conditions for equivalence between $\ell^1$ and $\ell^0$ minimization", CSL Technical Report UILU-ENG-07-2208, Univ. of Illinois, Urbana-Champaign 2007.
  14. H. Avron, A. Sharf, C. Greif and D. Cohen-Or, "$\ell_1$-Sparse Reconstruction of Sharp Point Set Surfaces", ACM Transactions on Graphics, 29(5): 135:1-135:12, 2010.
  15. E. Candes, M. B. Wakin and S. P. Boyd, "Enhancing Sparsity by Reweighted $\ell_1$ Minimization", Journal of Fourier Analysis and Applications, 14(56): 877-905, 2008. https://doi.org/10.1007/s00041-008-9045-x
  16. R. Wang, Z. Yang, L. Liu, J. Deng and F. Chen, "Decoupling noise and features via weighted $\ell_1$-analysis compressed sensing", ACM Transactions on Graphics, 33(2): 18:1-18:12, 2014.
  17. J. Digne, R. Chaine and S. Valette, "Self-Similarity for Accurate Compression of Point Sampled Surfaces", Computer Graphics Forum, 33(2): 155-164, 2014. https://doi.org/10.1111/cgf.12305
  18. S. Xiong, J. Zhang, J. Zheng, J. Cai and L. Liu, "Robust Surface Reconstruction via Dictionary Learning", ACM Transactions on Graphics, 33(6): 201:1-201:12, 2014.
  19. M. Aharon, M. Elad and A. Bruckstein, "K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation", IEEE Transactions on Signal Processing, 54(11): 4311-4322, 2006. https://doi.org/10.1109/TSP.2006.881199
  20. K. M. Koh, S. J. Kim and S. Boyd, "An Interior-Point Method for Large-Scale $\ell_1$-Regularized Logistic Regression", Journal of Machine Learning Research, 8: 1519-1555, 2007.
  21. l1_ls : Simple Matlab Solver for l1-regularized Least Squares Problems, http://web.stanford.edu/-boyd/l1_ls/
  22. Libigl, https://github.com/libigl/libigl