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Efficient Polyhedral Modeling from Silhouettes
March 2009 (vol. 31 no. 3)
pp. 414-427
Jean-Sébastien Franco, LaBRI CNRS-INRIA Sud-Ouest-Equipe IPARLA, France
Edmond Boyer, INRIA Rhône-Alpes, France
Modeling from silhouettes is a popular and useful topic in computer vision. Many methods exist to compute the surface of the visual hull from silhouettes, but few address the problem of ensuring sane topological properties of the surface, such as manifoldness. This article provides an efficient algorithm to compute such a surface in the form of a polyhedral mesh. It relies on a small number of geometric operations to compute a visual hull polyhedron in a single pass. Such simplicity enables the algorithm to combine the advantages of being fast, producing pixel-exact surfaces, and repeatably yield manifold and watertight polyhedra in general experimental conditions with real data, as verified with all datasets tested. The algorithm is fully described, its complexity analyzed and modeling results given.

[1] J. Isidoro and S. Sclaroff, “Stochastic Refinement of the Visual Hull to Satisfy Photometric and Silhouette Consistency Constraints,” Proc. Ninth Int'l Conf. Computer Vision, pp. 1335-1342, 2003.
[2] Y. Furukawa and J. Ponce, “Carved Visual Hulls for Image-Based Modeling,” Proc. European Conf. Computer Vision, 2006.
[3] S.N. Sinha and M. Pollefeys, “Multi-View Reconstruction Using Photo-Consistency and Exact Silhouette Constraints: A Maximum-Flow Formulation,” Proc. 10th Int'l Conf. Computer Vision, Oct. 2005.
[4] A. Laurentini, “The Visual Hull Concept for Silhouette-Based Image Understanding,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 2, pp. 150-162, Feb. 1994.
[5] B.G. Baumgart, “Geometric Modeling for Computer Vision,” PhD dissertation, aIM-249, STAN-CS-74-463, Computer Science Dept., Stanford Univ., Oct. 1974.
[6] S. Lazebnik, E. Boyer, and J. Ponce, “On Computing Exact Visual Hulls of Solids Bounded by Smooth Surfaces,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 156-161, Dec. 2001.
[7] S. Laveau and O. Faugeras, “Oriented Projective Geometry for Computer Vision,” Proc. Fourth European Conf. Computer Vision, 1996.
[8] W. Matusik, C. Buehler, R. Raskar, S. Gortler, and L. McMillan, “Image Based Visual Hulls,” Proc. ACM SIGGRAPH '00, ACM Computer Graphics, pp. 369-374, 2000.
[9] G. Cheung, T. Kanade, J.-Y. Bouguet, and M. Holler, “A Real Time System for Robust 3D Voxel Reconstruction of Human Motions,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp.714-720, June 2000.
[10] W. Martin and J. Aggarwal, “Volumetric Description of Objects from Multiple Views,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 2, pp. 150-158, 1983.
[11] C. Chien and J. Aggarwal, “Volume/Surface Octress for the Representation of Three-Dimensional Objects,” Computer Vision, Graphics, and Image Processing, vol. 36, no. 1, pp. 100-113, 1986.
[12] M. Potmesil, “Generating Octree Models of 3D Objects from Their Silhouettes in a Sequence of Images,” Computer Vision, Graphics, and Image Processing, vol. 40, no. 1, pp. 1-29, 1987.
[13] S.K. Srivastava, “Octree Generation from Object Silhouettes in Perspective Views,” Computer Vision, Graphics, and Image Processing, vol. 49, no. 1, pp. 68-84, 1990.
[14] R. Szeliski, “Rapid Octree Construction from Image Sequences,” Computer Vision, Graphics, and Image Processing, vol. 58, no. 1, pp.23-32, 1993.
[15] W. Niem, “Automatic Modeling of 3D Natural Objects from Multiple Views,” Proc. European Workshop Combined Real and Synthetic Image Processing for Broadcast and Video Production, 1994.
[16] E. Boyer and J.-S. Franco, “A Hybrid Approach for Computing Visual Hulls of Complex Objects,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 695-701, 2003.
[17] J. Koenderink, “What Does the Occluding Contour Tell Us about Solid Shape?” Perception, vol. 13, pp. 321-330, 1984.
[18] P. Giblin and R. Weiss, “Reconstruction of Surfaces from Profiles,” Proc. First Int'l Conf. Computer Vision, pp. 136-144, 1987.
[19] R. Cipolla and A. Blake, “Surface Shape from the Deformation of Apparent Contours,” Int'l J. Computer Vision, vol. 9, pp. 83-112, 1992.
[20] R. Vaillant and O. Faugeras, “Using Extremal Boundaries for 3-D Object Modeling,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 157-173, Feb. 1992.
[21] E. Boyer and M.-O. Berger, “3D Surface Reconstruction Using Occluding Contours,” Int'l J. Computer Vision, vol. 22, no. 3, pp.219-233, 1997.
[22] G. Cross and A. Zisserman, “Quadric Reconstruction from Dual-Space Geometry,” Proc. Sixth Int'l Conf. Computer Vision, 1998.
[23] K. Kang, J. Tarel, R. Fishman, and D. Cooper, “A Linear Dual-Space Approach to 3D Surface Reconstruction from Occluding Contours,” Proc. Eighth Int'l Conf. Computer Vision, 2001.
[24] M. Brand, K. Kang, and D.B. Cooper, “Algebraic Solution for the Visual Hull,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 30-35, 2004.
[25] C. Liang and K.-Y.K. Wong, “Complex 3D Shape Recovery Using a Dual-Space Approach,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 878-884, 2005.
[26] S. Sullivan and J. Ponce, “Automatic Model Construction and Pose Estimation from Photographs Using Triangular Splines,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 10, pp.1091-1097, Oct. 1998.
[27] W. Matusik, C. Buehler, and L. McMillan, “Polyhedral Visual Hulls for Real-Time Rendering,” Proc. Eurographics Workshop Rendering, 2001.
[28] M. Li, M. Magnor, and H.-P. Seidel, “Hardware-Accelerated Visual Hull Reconstruction and Rendering,” Proc. Graphics Interface, 2003.
[29] M. Li, M. Magnor, and H.-P. Seidel, “A Hybrid Hardware-Accelerated Algorithm for High Quality Rendering of Visual Hulls,” Proc. Conf. Graphics Interface, pp. 41-48, 2004.
[30] S. Lazebnik, “Projective Visual Hulls,” master's thesis, Univ. of Illinois, Urbana-Champaign, 2002.
[31] K. Kutulakos and S. Seitz, “A Theory of Shape by Space Carving,” Int'l J. Computer Vision, vol. 38, no. 3, pp. 199-218, 2000.
[32] S. Seitz and C. Dyer, “Photorealistic Scene Reconstruction by Voxel Coloring,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1067-1073, 1997.
[33] G. Slabaugh, B. Culbertson, T. Malzbender, and R. Schafe, “A Survey of Methods for Volumetric Scene Reconstruction from Photographs,” Proc. Int'l Workshop Volume Graphics, 2001.
[34] C. Dyer, “Volumetric Scene Reconstruction from Multiple Views,” Foundations of Image Understanding, L. Davis, ed., pp. 469-489, 2001.
[35] I. Debled-Rennesson and J. Reveillès, “A Linear Algorithm for Segmentation of Digital Curves,” Int'l J. Pattern Recognition and Artificial Intelligence, vol. 9, no. 4, pp. 635-662, 1995.
[36] S. Lazebnik, Y. Furukawa, and J. Ponce, “Projective Visual Hulls,” Int'l J. Computer Vision, vol. 74, no. 2, pp. 137-165, 2007.
[37] A.A.G. Requicha and H.B. Voelcker, “Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms,” Proc. IEEE, vol. 73, no. 1, pp. 30-44, Jan. 1985.
[38] C.M. Hoffmann, J.E. Hopcroft, and M.E. Karasick, “Robust Set Operations on Polyhedral Solids,” IEEE Computer Graphics and Applications, vol. 9, no. 6, pp. 50-59, 1989.
[39] S. Fortune, “Polyhedral Modelling with Exact Arithmetic,” Proc. Third ACM Symp. Solid Modeling and Applications, pp. 225-234, 1995.
[40] P. Hachenberger and L. Kettner, “Boolean Operations on 3D Selective NEF Complexes: Optimized Implementation and Experiments,” Proc. ACM Symp. Solid and Physical Modeling, pp. 163-174, 2005.
[41] R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, June 2000.
[42] O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, 1993.
[43] G. Cheung, S. Baker, and T. Kanade, “Visual Hull Alignment and Refinement across Time: A 3D Reconstruction Algorithm Combining Shape-from-Silhouette with Stereo,” Proc. IEEE Conf. Computer Vision and Pattern Recognition), 2003.
[44] Opengl Utility Library (glu), http:/, 2008.
[45] W. Matusik, L. McMillan, and S. Gortler, “An Efficient Visual Hull Computation Algorithm,” technical report, MIT LCS, Feb. 2002.
[46] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Surface Reconstruction from Unorganized Points,” ACM Computer Graphics, Proc. ACM SIGGRAPH '92, vol. 26, no. 2, pp. 71-78, July 1992.
[47] C.M. Hoffmann, Geometric and Solid Modeling. Morgan Kaufmann, 1989.

Index Terms:
Computer vision, Vision and Scene Understanding, 3D/stereo scene analysis, Modeling from video
Jean-Sébastien Franco, Edmond Boyer, "Efficient Polyhedral Modeling from Silhouettes," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 3, pp. 414-427, March 2009, doi:10.1109/TPAMI.2008.104
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