Shape Reconstruction from 3D and 2D Data Using PDE-Based Deformable Surfaces

  • Ye Duan
  • Liu Yang
  • Hong Qin
  • Dimitris Samaras
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3023)


In this paper, we propose a new PDE-based methodology for deformable surfaces that is capable of automatically evolving its shape to capture the geometric boundary of the data and simultaneously discover its underlying topological structure. Our model can handle multiple types of data (such as volumetric data, 3D point clouds and 2D image data), using a common mathematical framework. The deformation behavior of the model is governed by partial differential equations (e.g. the weighted minimal surface flow). Unlike the level-set approach, our model always has an explicit representation of geometry and topology. The regularity of the model and the stability of the numerical integration process are ensured by a powerful Laplacian tangential smoothing operator. By allowing local adaptive refinement of the mesh, the model can accurately represent sharp features. We have applied our model for shape reconstruction from volumetric data, unorganized 3D point clouds and multiple view images. The versatility and robustness of our model allow its application to the challenging problem of multiple view reconstruction. Our approach is unique in its combination of simultaneous use of a high number of arbitrary camera views with an explicit mesh that is intuitive and easy-to-interact-with. Our model-based approach automatically selects the best views for reconstruction, allows for visibility checking and progressive refinement of the model as more images become available. The results of our extensive experiments on synthetic and real data demonstrate robustness, high reconstruction accuracy and visual quality.


Point Cloud Collision Detection Deformable Model Volumetric Data Subdivision Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amenta, N., Bern, M., Kamvysselis, M.: A new voronoi-based surface reconstruction algorithm. In: SIGGRAPH, pp. 415–421 (1998)Google Scholar
  2. 2.
    Besl, P., McKay, H.: A method for registration of 3d shapes. PAMI (1992)Google Scholar
  3. 3.
    De Bonet, J.S., Poxels, P.V.: Probabilistic voxelized volume reconstruction. In: ICCV, pp. 418–425 (1999)Google Scholar
  4. 4.
    Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3d objects with radial basis functions. In: SIGGRAPH (2001)Google Scholar
  5. 5.
    Caselles, V., Kimmel, R., Sapiro, G., Sbert, C.: Minimal surfaces based object segmentation. PAMI 19 (1997)Google Scholar
  6. 6.
    Charles. Smooth subdivision surfaces based on triangles. Master’s thesis, Mathematics, Univ. of Utah (August 1987)Google Scholar
  7. 7.
    Culbertson, B., Malzbender, T., Slabaugh, G.: Generalized voxel coloring. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, p. 100. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    De Carlo, D., Metaxas, D.N.: Blended deformable models. PAMI (1996)Google Scholar
  9. 9.
    Deriche, R., Bouvin, C., Faugeras, O.D.: Front propagation and level-set approach for geodesic active stereovision. In: Chin, R., Pong, T.-C. (eds.) ACCV 1998. LNCS, vol. 1351, pp. 1: 640–647. Springer, Heidelberg (1998)Google Scholar
  10. 10.
    Dinh, H.Q., Slabaugh, G., Turk, G.: Reconstructing surfaces using anisotropic basis functions. In: ICCV (2001)Google Scholar
  11. 11.
    Edelsbrunner, H., Mucke, E.P.: Three-dimensional alpha shapes. ACM Transactions on Graphics 13, 43–72 (1994)zbMATHCrossRefGoogle Scholar
  12. 12.
    Faugeras, O., Keriven, R.: Complete dense stereovision using level set methods. In: Burkhardt, H.-J., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1406, pp. 379–393. Springer, Heidelberg (1998)Google Scholar
  13. 13.
    Fua, P.: From multiple stereo views to multiple 3d surfaces. IJCV 24, 19–35 (1997)CrossRefGoogle Scholar
  14. 14.
    Zhao, H.K., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: VLSM Workshop (July 2001)Google Scholar
  15. 15.
    Hoppe, H., De Rose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: SIGGRAPH (1992)Google Scholar
  16. 16.
    Jin, H., Soatto, S., Yezzi, A.: Multi-view stereo beyond lambert. In: CVPR (2003)Google Scholar
  17. 17.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. IJCV, 321–331 (1988)Google Scholar
  18. 18.
    Kimmel, R.: 3d shape reconstruction from autostereograms and stereo. Journal of Visual Communication and Image Representation 13, 324–333 (2002)CrossRefGoogle Scholar
  19. 19.
    Kimmel, R., Sethian, J.A.: Computing geodesic paths on manifolds. Proceedings of National Academy of Sciences, 8431–8435 (July 1998)Google Scholar
  20. 20.
    Kobbelt, L., Bareuther, T., Seidel, H.-P.: Multiresolution shape deformations for meshes with dynamic vertex connectivity. In: Eurographics, pp. 249–260 (2000)Google Scholar
  21. 21.
    Kutulakos, K.N., Seitz, S.M.: A theory of shape by space carving. In: ICCV (1999)Google Scholar
  22. 22.
    Lachaud, J.-O., Montanvert, A.: Deformable meshes with automated topology changes for coarse-to-fine 3d surface extraction. Medical Image Analysis 3(2), 187–207 (1999)CrossRefGoogle Scholar
  23. 23.
    Lorensen, W., Cline, H.: Marching cubes: A high resolution 3d surface construction algorithm. In: SIGGRAPH (1997)Google Scholar
  24. 24.
    Malladi, R., Sethian, J., Vemuri, B.: Shape modeling with front propagation: A level set approach. PAMI 17(2) (1995)Google Scholar
  25. 25.
    McInerney, T., Terzopoulos, D.: Deformable models in medical image analysis: a survey. Medical Image Analysis 1(2) (1996)Google Scholar
  26. 26.
    McInerney, T., Terzopoulos, D.: Topology adaptive deformable surfaces for medical image volume segmentation. In: TMI, pp. 840–850 (1999)Google Scholar
  27. 27.
    Metaxas, D., Terzopoulos, D.: Shape and nonrigid motion estimation through physics-based synthesis. PAMI 15(6) (1993)Google Scholar
  28. 28.
    Miller, J.V., Breen, D.E., Lorensen, W.E., O’Bara, R.M., Wozny, M.J.: Geometric deformed models: a method for extracting closed geometric models from volume data. In: SIGGRAPH, pp. 217–226 (1991)Google Scholar
  29. 29.
    Pollefeys, M., Van Gool, L.J.: From images to 3d models. CACM 7, 50–55 (2002)Google Scholar
  30. 30.
    Rusinkiewicz, S., Levoy, M.: Efficient variants of the icp algorithm. In: Proceedings of 3D Digital Imaging and Modeling, pp. 145–152 (2001)Google Scholar
  31. 31.
    Rusinkiewicz, S., Hall-Holt, O.A., Levoy, M.: Real-time 3d model acquisition. ACM Transactions on Graphics 21(3), 438–446 (2002)CrossRefGoogle Scholar
  32. 32.
    Seitz, S.M., Dyer, C.M.: Photorealistic scene reconstruction by voxel coloring. IJCV 35(2), 1–23 (1999)CrossRefGoogle Scholar
  33. 33.
    Slabaugh, G.G., Schafer, R.W., Hans, M.C.: Multi-resolution space carving using level sets methods. In: ICIP (2002)Google Scholar
  34. 34.
    Taylor, C.J., Jelinek, D.: Structure and motion from line segments in multiple images. PAMI 17(11) (1995)Google Scholar
  35. 35.
    Trucco, E., Verri, A.: Introductory Techniques for 3-D Computer Vsion. Prentice Hall, Englewood Cliffs (1998)Google Scholar
  36. 36.
    Wood, Z., Desbrun, M., Schroder, P., Breen, D.: Semi-regular mesh extraction from volumes. In: Proceedings of IEEE Visualization, pp. 275–282 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ye Duan
    • 1
  • Liu Yang
    • 2
  • Hong Qin
    • 2
  • Dimitris Samaras
    • 2
  1. 1.Department of Computer ScienceUniversity of Missouri at ColumbiaColumbiaUSA
  2. 2.Center for Visual Computing, Department of Computer ScienceState University of New York at Stony BrookNYUSA

Personalised recommendations