The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.04 - July/August (2010 vol.16)
pp: 636-646
Rasmus R. Paulsen , Technical University of Denmark, Lyngby
Jakob Andreas Bærentzen , Technical University of Denmark, Lyngby
Rasmus Larsen , Technical University of Denmark, Lyngby
ABSTRACT
A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse Cholesky factorization, and a multiscale iterative optimization scheme. The method is demonstrated on a set of scanned human heads and, both in terms of accuracy and the ability to close holes, the proposed method is shown to have similar or superior performance when compared to current state-of-the-art algorithms.
INDEX TERMS
Bayesian approach, implicit surface, Markov random field, mesh generation, surface reconstruction.
CITATION
Rasmus R. Paulsen, Jakob Andreas Bærentzen, Rasmus Larsen, "Markov Random Field Surface Reconstruction", IEEE Transactions on Visualization & Computer Graphics, vol.16, no. 4, pp. 636-646, July/August 2010, doi:10.1109/TVCG.2009.208
REFERENCES
[1] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, "Surface Reconstruction from Unorganized Points," Proc. ACM SIGGRAPH, pp. 71-78, 1992.
[2] W.E. Lorensen and H.E. Cline, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm," Proc. ACM SIGGRAPH '87, vol. 21, no. 4, pp. 163-169, July 1987.
[3] G. Treece, R. Prager, and A. Gee, "Regularised Marching Tetrahedra: Improved Iso-Surface Extraction," Computers & Graphics, vol. 23, no. 4, pp. 583-598, 1999.
[4] J. Bloomenthal, "An Implicit Surface Polygonizer," Proc. Graphics Gems IV, pp. 324-349, 1994.
[5] B. Curless and M. Levoy, "A Volumetric Method for Building Complex Models from Range Images," Proc. ACM SIGGRAPH, pp. 303-312, 1996.
[6] 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," Proc. ACM SIGGRAPH, pp. 67-76, 2001.
[7] Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, and H. Seidel, "Multi-Level Partition of Unity Implicits," Proc. Int'l Conf. Computer Graphics and Interactive Techniques, pp. 463-470, 2003.
[8] M. Kazhdan, M. Bolitho, and H. Hoppe, "Poisson Surface Reconstruction," Proc. Symp. Geometry Processing, pp. 61-70, 2006.
[9] M. Kazhdan, "Reconstruction of Solid Models from Oriented Point Sets," Proc. Third Eurographics Symp. Geometry Processing, 2005.
[10] O. Schall, A. Belyaev, and H. Seidel, "Error-Guided Adaptive Fourier-Based Surface Reconstruction," Computer-Aided Design, vol. 39, no. 5, pp. 421-426, 2007.
[11] B. Jakobsen, J.A. Bærentzen, and N.J. Christensen, "Variational Volumetric Surface Reconstruction from Unorganized Points," Proc. IEEE/EG Int'l Symp. Volume Graphics, Sept. 2007.
[12] S. Geman and D. Geman, "Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, Nov. 1984.
[13] J. Besag, "Towards Bayesian Image Analysis," J. Applied Statistics, vol. 16, no. 3, pp. 395-407, 1989.
[14] J. Besag, "On the Statistical Analysis of Dirty Pictures," J. Royal Statistical Soc., Series B, vol. 48, no. 3, pp. 259-302, 1986.
[15] D. Geman, "Random Fields and Inverse Problems in Imaging," Saint-Flour Lectures, Springer-Verlag, pp. 113-193, 1990.
[16] R. Larsen, K. Conradsen, and B.K. Ersbøll, "Estimation of Dense Image Flow Fields in Fluids," IEEE Trans. Geoscience and Remote Sensing, vol. 36, no. 1, pp. 256-264, Jan. 1998.
[17] R.R. Paulsen and K.B. Hilger, "Shape Modelling Using Markov Random Field Restoration of Point Correspondences," Proc. Information Processing in Medical Imaging, vol. 2732, pp. 1-12, 2003.
[18] G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods—A Mathematical Introduction, second ed., vol. 27. Springer-Verlag, 2003.
[19] G. Storvik, "Bayesian Surface Reconstruction from Noisy Images," Proc. 28th Symp. Interface (Interface), vol. 28, pp. 91-9, 1997.
[20] P. Jenke, M. Wand, M. Bokeloh, A. Schilling, and W. Strasser, "Bayesian Point Cloud Reconstruction," Computer Graphics Forum, vol. 25, no. 3, pp. 379-388, 2006.
[21] J. Diebel, S. Thrun, and M. Brünig, "A Bayesian Method for Probable Surface Reconstruction and Decimation," ACM Trans. Graphics, vol. 25, no. 1, pp. 39-59, 2006.
[22] Q. Huang, B. Adams, and M. Wand, "Bayesian Surface Reconstruction via Iterative Scan Alignment to an Optimized Prototype," Proc. Fifth Eurographics Symp. Geometry Processing, pp. 213-223, 2007.
[23] N. Moretto and R. Frezza, "Bayesian Surface Reconstruction," Proc. Second Int'l Symp. 3D Data Processing, Visualization and Transmission (3DPVT '04), pp. 235-241, 2004.
[24] T. Tasdizen and R. Whitaker, "Higher-Order Nonlinear Priors for Surface Reconstruction," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 7, pp. 878-891, July 2004.
[25] H.-K. Zhao, S. Osher, and R. Fedkiw, "Fast Surface Reconstruction Using the Level Set Method," Proc. IEEE Workshop Variational and Level Set Methods in Computer Vision, 2003.
[26] R. Whitaker, "A Level-Set Approach to 3D Reconstruction from Range Data," Int'l J. Computer Vision, vol. 29, no. 3, pp. 203-232, 1998.
[27] J. Gomes and O. Faugeras, "Level Sets and Distance Functions," Lecture Notes in Computer Science, pp. 588-602, Springer, 2000.
[28] J. Verdera, V. Caselles, M. Bertalmio, and G. Sapiro, "Inpainting Surface Holes," Proc. Int'l Conf. Image Processing (ICIP '03), vol. 2, 2003.
[29] U. Clarenz, U. Diewald, G. Dziuk, M. Rumpf, and R. Rusu, "A Finite Element Method for Surface Restoration with Smooth Boundary Conditions," Computer Aided Geometric Design, vol. 21, no. 5, pp. 427-446, 2004.
[30] V. Caselles, G. Haro, G. Sapiro, and J. Verdera, "On Geometric Variational Models for Inpainting Surface Holes," Computer Vision and Image Understanding, vol. 111, no. 3, pp. 351-373, 2008.
[31] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C.T. Silva, "Point Set Surfaces," Proc. Conf. Visualization (VIS '01), pp. 21-28, 2001.
[32] S. Fleishman, D. Cohen-Or, and C. Silva, "Robust Moving Least-Squares Fitting with Sharp Features," Proc. Int'l Conf. Computer Graphics and Interactive Techniques, pp. 544-552, 2005.
[33] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems," J. Royal Statistical Soc., Series B, vol. 36, pp. 192-236, 1974.
[34] D. Terzopoulos, "Regularization of Inverse Visual Problems Involving Discontinuities," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 4, pp. 413-242, July 1986.
[35] M. Jones, J. Bærentzen, and M. Sramek, "3D Distance Fields: A Survey of Techniques and Applications," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 4, pp. 518-599, July/Aug. 2006.
[36] J. Shewchuk, "An Introduction to the Conjugate Gradient Method without the Agonizing Pain," technical report, School of Computer Science, Carnegie Mellon Univ., 1994.
[37] P. Frandsen, K. Jonasson, H. Nielsen, and O. Tingleff, "Unconstrained Optimization," third ed., technical report, Informatics and Mathematical Modelling, Technical Univ. of Denmark, Mar. 2004.
[38] W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C: The Art of Scientific Computing. Cambridge Univ. Press, 2002.
[39] T.A. Davis and W.W. Hager, "Row Modifications of a Sparse Cholesky Factorization," SIAM J. Matrix Analysis and Applications, vol. 26, no. 3, pp. 621-639, 2005.
[40] M. Botsch and L. Kobbelt, "A Remeshing Approach to Multiresolution Modeling," Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 185-192, 2004.
[41] P. Hammond, T. Hutton, J. Allanson, L. Campbell, R. Hennekam, S. Holden, M. Patton, A. Shaw, I. Temple, and M. Trotter, "3D Analysis of Facial Morphology," Am. J. Medical Genetics, vol. 126, no. 4, pp. 339-348, 2004.
[42] B. Katz, "Boundary Element Method Calculation of Individual Head-Related Transfer Function. I. Rigid Model Calculation," J. Acoustical Soc. of Am., vol. 110, pp. 2440-2448, 2001.
[43] L. Velho, J. Gomes, and L. de Figueiredo, Implicit Objects in Computer Graphics. Springer, 2002.
[44] P. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. Soc. for Industrial Math., 1998.
[45] M. Klodt, T. Schoenemann, K. Kolev, M. Schikora, and D. Cremers, "An Experimental Comparison of Discrete and Continuous Shape Optimization Methods," Proc. 10th European Conf. Computer Vision: Part I, pp. 332-345, 2008.
38 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool