This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Implicit Meshes for Surface Reconstruction
February 2006 (vol. 28 no. 2)
pp. 328-333
Deformable 3D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, but fitting them involves minimizing a nondifferentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but are harder to meaningfully deform and render. Here, we propose a method that combines the strength of both approaches. It relies on a technique that can turn a completely arbitrary triangulated mesh, such as one taken from the Web, into an implicit surface that closely approximates it and can deform in tandem with it. This allows both automated algorithms to take advantage of the attractive properties of implicit surfaces for fitting purposes and people to use standard deformation tools they feel comfortable for interaction and animation purposes. We demonstrate the applicability of our technique to modeling the human upper-body, including face, neck, shoulders, and ears, from noisy stereo and silhouette data.

[1] N. Amenta and Y. Kil, “Defining Point-Set Surfaces,” Proc. SIGGRAPH Computer Graphics, pp. 264-270, July 2004.
[2] C. Bajaj and I. Ihm, “$C^{1}$ Smoothing of Polyhedra with Implicit Algebraic Splines,” Proc. SIGGRAPH Computer Graphics, vol. 26, no. 2, pp. 79-88, 1992.
[3] A.H. Barr, “Local and Global Deformations of Solid Primitives,” Proc. SIGGRAPH Computer Graphics, pp. 21-30, Sept. 1984.
[4] V. Blanz and T. Vetter, “A Morphable Model for the Synthesis of 3D Faces,” Proc. SIGGRAPH Computer Graphics, Aug. 1999.
[5] J.F. Blinn, “A Generalization of Algebraic Surface Drawing,” ACM Trans. Graphics, vol. 1, no. 3, pp. 235-256, 1982.
[6] I. Cohen, L.D. Cohen, and N. Ayache, “Introducing New Deformable Surfaces to Segment 3D Images,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 738-739, 1991.
[7] S. Coquillart, “Extended Free-Form Deformation: A Sculpturing Tool for 3D Geometric Modeling,” Proc. SIGGRAPH Computer Graphics, vol. 24, no. 4, pp. 187-196, 1990.
[8] M. Desbrun and M.P. Gascuel, “Animating Soft Substances with Implicit Surfaces,” Proc. SIGGRAPH Computer Graphics, pp. 287-290, 1995.
[9] M. Dimitrijević, S. Ilić, and P. Fua, “Accurate Face Models from Uncalibrated and Ill-Lit Video Sequences,” Proc. Conf. Computer Vision and Pattern Recognition, June 2004.
[10] Y. Duan, L. Yang, H. Qin, and D. Samaras, “Shape Reconstruction from 3D and 2D Data Using PDE-Based Deformable Surfaces,” Proc. European Conf. Computer Vision, vol. 3, pp. 238-251, May 2004.
[11] M. Eck and H. Hoppe, “Automatic Reconstruction of B-Spline Surfaces of Arbitrary Topological Type,” Proc. SIGGRAPH Computer Graphics, pp. 325-334, 1996.
[12] J.C. Carr et al., “Reconstruction and Representation of 3d Objects with Radial Basis Functions,” Proc. SIGGRAPH Computer Graphics, vol. 2, 2001.
[13] J.C. Carr et al., “Smooth Surface Reconstruction from Noisy Range Data,” Proc. ACM GRAPHITE, pp. 119-126, 2003.
[14] F.P. Ferrie, J. Lagarde, and P. Whaite, “Recovery of Volumetric Object Descriptions from Laser Rangefinder Images,” Proc. European Conf. Computer Vision, Apr. 1992.
[15] P. Fua, “Regularized Bundle-Adjustment to Model Heads from Image Sequences without Calibration Data,” Int'l J. Computer Vision, vol. 38, no. 2, pp. 153-171, July 2000.
[16] H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jun, J. McDonald, J. Schweitzer, and W. Stuetzle, “Piecewise Smooth Surface Reconstruction,” Proc. SIGGRAPH Computer Graphics, pp. 295-302, 1994.
[17] S. Ilić and P. Fua, “Using Dirichlet Free Form Deformation to Fit Deformable Models to Noisy 3-D Data,” Proc. European Conf. Computer Vision, May 2002.
[18] S. Ilić and P. Fua, “Implicit Mesh Models for Modeling and Tracking,” Proc. Conf. Computer Vision and Pattern Recognition, June 2003.
[19] S. Ilić and P. Fua, “Implicit Meshes for Surface Reconstruction,” Technical Report IC/2004/25, EPFL, 2004.
[20] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” Int'l J. Computer Vision, vol. 1, no. 4, pp. 321-331, 1988.
[21] V. Krishnamurthy and M. Levoy, “Fitting Smooth Surfaces to Dense Polygon Meshes,” Proc. SIGGRAPH Computer Graphics, pp. 313-324, 1996.
[22] D. Levin, “Mesh-Independent Surface Interpolation,” Geometric Modeling for Scientific Visualization, Brunnett, Hamann, and Mueller, eds., pp. 37-49, Springer-Verlag, 2003.
[23] N. Litke, A. Levin, and P. Schröder, “Fitting Subdivision Surfaces,” Proc. Conf. Visualization, pp. 319-324, 2001.
[24] D.G. Lowe, “Fitting Parameterized Three-Dimensional Models to Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 441-450, 1991.
[25] D. Metaxas and D. Terzopoulos, “Shape and Nonrigid Motion Estimation through Physics-Based Synthesis,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 6, pp. 580-591, June 1991.
[26] L. Moccozet and N. Magnenat-Thalmann, “Dirichlet Free-Form Deformation and Their Application to Hand Simulation,” Computer Animation, 1997.
[27] Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, and H.-P. Seidel, “Multi-Level Partition of Unity Implicits,” Proc. SIGGRAPH Computer Graphics, vol. 22, no. 2, pp. 463-470, 2003.
[28] A. Pentland and S. Sclaroff, “Closed-Form Solutions for Physically Based Shape Modeling and Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 715-729, 1991.
[29] R. Plänkers and P. Fua, “Articulated Soft Objects for Multi-View Shape and Motion Capture,” IEEE Trans. Pattern Analysis and Machine Intelligence, 2003.
[30] S. Roy and I.J. Cox, “A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem,” Proc. Int'l Conf. Computer Vision, pp. 492-499, 1998.
[31] T.W. Sederberg and S.R. Parry, “Free-Form Deformation of Solid Geometric Models,” Proc. SIGGRAPH Computer Graphics, vol. 20, p. 4, 1986.
[32] C. Shen, J.F. O'Brien, and J.R. Shewchuk, “Interpolating and Approximating Implicit Surfaces from Polygon Soup,” Proc. ACM SIGGRAPH, Aug. 2004.
[33] R. Sibson, “A Vector Identity for the Dirichlet Tessellation,” Proc. Math. Cambridge Philosophical Soc., pp. 151-155, 1980.
[34] E.M. Stokely and S.Y. Wu, “Surface Parameterization and Curvature Measurement of Arbitrary 3D Objects: Five Practical Methods,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 8, pp. 833-839, Aug. 1992.
[35] S. Sullivan, L. Sandford, and J. Ponce, “Using Geometric Distance Fits for 3D Object Modeling and Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 12, pp. 1183-1196, Dec. 1994.
[36] R. Szeliski and D. Tonnesen, “Surface Modeling with Oriented Particle Systems,” Proc. SIGGRAPH Computer Graphics, vol. 26, pp. 185-194, July 1992.
[37] D. Terzopoulos and D. Metaxas, “Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 703-714, 1991.
[38] D. Terzopoulos and M. Vasilescu, “Sampling and Reconstruction with Adaptive Meshes,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 70-75, 1991.
[39] G. Turk and J.F. O'Brien, “Shape Transformation Using Variational Implicit Functions,” Proc. SIGGRAPH Computer Graphics, vol. 33, pp. 335-342, 1999.
[40] B. Wyvill and K. van Overveld, “Warping as a Modelling Tool for CSG/Implicit Models,” Proc. Shape Modelling Conf., pp. 205-214, Mar. 1997.

Index Terms:
Index Terms- Computer vision, reconstruction, surface fitting, modeling, optimization.
Citation:
Slobodan Ilic, Pascal Fua, "Implicit Meshes for Surface Reconstruction," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 2, pp. 328-333, Feb. 2006, doi:10.1109/TPAMI.2006.37
Usage of this product signifies your acceptance of the Terms of Use.