“Piecewise smooth surface reconstruction” by Hoppe, DeRose, Duchamp, Halstead, Jin, et al. …

  • ©Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark A. Halstead, Hubert Jin, John McDonald Jr., Jean Schweitzer, and Werner Stuetzle


    We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering—the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data.A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.


    1. Ruud M. Bolle and Baba C. Vemuri. On three-dimensional surface reconstruction methods. IEEE Trans. Pat. Anal. Mach. Intell., 13(1):13, January 1991.
    2. James F. Brinkley. Knowledge-driven ultrasonic three-dimensional or-gan modeling. IEEE Trans. Pat. Anal. Mach. Intell., 7(4):431-441, July 1985.
    3. E. Catmull and J. Clark. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design, 10:350-355, September 1978.
    4. T. DeRose, H. Hoppe, T. Duchamp, J. McDonald, and W. Stuetzle. Fitting of surfaces to scattered data. SPIE, 1830:212-220, 1992.
    5. D. Doo and M. Sabin. Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design, 10(6):356-360, September 1978.
    6. G. Farin. Curves and Surfaces for Computer Aided Geometric Design. Academic Press, 3rd edition, 1992.
    7. Ardeshir Goshtasby. Surface reconstruction from scattered measure-ments. SPIE, 1830:247-256, 1992.
    8. Mark Halstead, Michael Kass, and Tony DeRose. Efficient, fair in-terpolation using Catmull-Clark surfaces. Computer Graphics (SIG-GRAPH ’93 Proceedings), pages 35-44, August 1993.
    9. H. Hoppe, T. DeRose, T. Duchamp, H. Jin, J. McDonald, and W. Stuet-zle. Piecewise smooth surface reconstruction. TR 94-01-01, Dept. of Computer Science and Engineering, University of Washington, Jan-uary 1994.
    10. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Surface reconstruction from unorganized points. Computer Graphics (SIGGRAPH ’92 Proceedings), 26(2):71-78, July 1992.
    11. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. Mesh optimization. Computer Graphics (SIGGRAPH ’93 Proceed-ings), pages 19-26, August 1993.
    12. Hugues Hoppe. Surface reconstruction from unorganized points. PhD thesis, Department of Computer Science and Engineering, University of Washington, In preparation.
    13. Charles Loop. Smooth subdivision surfaces based on triangles. Mas-ter’s thesis, Department of Mathematics, University of Utah, August 1987.
    14. Michael Lounsbery, Stephen Mann, and Tony DeRose. Parametric surface interpolation. IEEE Computer Graphics and Applications, 12(5):45-52, September 1992. surface reconstruction pro-cedure surface models from un-organized determines the topo-logical and location of sharp new subdivision sur-face surface features such as Finally, we have demon-strated surface optimization pro-cedure from range data, and swept surfaces and including: model a wider va-riety darts meeting at corner. algorithms that allow implementations on parallel ar-chitectures. 12(5):45-52, September 1992.
    15. Ahmad H. Nasri. Polyhedral subdivision methods for free-form sur-faces. ACM Transactions on Graphics, 6(1):29-73, January 1987.
    16. Ahmad H. Nasri. Boundary-corner control in recursive-subdivision surfaces. Computer Aided Design, 23(6):405-410, July-August 1991.
    17. G. Nielson. A transfinite, visually continuous, triangular interpolant. In G. Farin, editor, Geometric Modeling: Algorithms and New Trends, pages 235-246. SIAM, 1987.
    18. Michael Plass and Maureen Stone. Curve-fitting with piecewise para-metric cubics. Computer Graphics (SIGGRAPH ’83 Proceedings), 17(3):229-239, July 1983.
    19. Ulrich Reif. A unified approach to subdivision algorithms. Mathema-tisches Institute A 92-16, Universit~ at Stuttgart, 1992.
    20. F. Schmitt, B.A. Barsky, and W. Du. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics (SIG-GRAPH ’86 Proceedings), 20(4):179-188, 1986.
    21. F. Schmitt, X. Chen, W. Du, and F. Sair. Adaptive approximation of range data using triangular patches. In P.J. Laurent, A. Le Mehaute, and L.L. Schumaker, editors, Curves and Surfaces. Academic Press, 1991.
    22. R. B. Schudy and D. H. Ballard. Model detection of cardiac cham-bers in ultrasound images. Technical Report 12, Computer Science Department, University of Rochester, 1978.
    23. R. B. Schudy and D. H. Ballard. Towards an anatomical model of heart motion as seen in 4-d cardiac ultrasound data. In Proceedings of the 6th Conference on Computer Applications in Radiology and Computer-Aided Analysis of Radiological Images, 1979.
    24. S. Sclaroff and A. Pentland. Generalized implicit functions for com-puter graphics. Computer Graphics (SIGGRAPH ’91 Proceedings), 25(4):247-250, July 1991.
    25. L. Shirman and C. S~ equin. Local surface interpolation with B~ ezier patches. Computer Aided Geometric Design, 4(4):279-296, 1988.
    26. R. Szeliski, D. Tonnesen, and D. Terzopoulos. Modeling surfaces of arbitrary topology with dynamicparticles. In 1993IEEE Computer So-ciety Conference on Computer Vision and Pattern Recognition, pages 82-87. IEEE Computer Society Press, 1993.
    27. R.C. Veltkamp. 3D computational morphology. Computer Graphics Forum, 12(3):116-127, 1993.

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