Browse > Article
http://dx.doi.org/10.15701/kcgs.2017.23.1.57

Geometry Reconstruction Using Dictionary Learning of 3D Shape Features  

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)
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.
Keywords
Geometry reconstruction; Dictionary learning; Compressed sensing;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI
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.   DOI
11 D. Ge, X. Jiang and Y. Ye, "A Note on the Complexity of $L_1$ Minimization", Mathematical Programming, 129(2): 285-299, 2011.   DOI
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.   DOI
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 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.
18 J. Digne, R. Chaine and S. Valette, "Self-Similarity for Accurate Compression of Point Sampled Surfaces", Computer Graphics Forum, 33(2): 155-164, 2014.   DOI
19 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.
20 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.   DOI
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