Advertisement

Free-Form Surface Description in Multiple Scales: Extension to Incomplete Surfaces

  • Nasser Khalili
  • Farzin Mokhtarian
  • Peter Yuen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1689)

Abstract

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Diffusion of the surface is achieved through convolutions of local parametrisations of the surface with a 2-D Gaussian filter. Our method for local parametrisation makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. During smoothing some surfaces can become very thin locally. Application of decimation followed by refinement removes very small/ thin triangles and segments those surfaces into parts which are then smoothed separately. Furthermore, surfaces with holes and surfaces that are not simply connected do not pose any problems. Our method is also more efficient than those techniques since 2-D rather than 3-D convolutions are employed. It is also argued that the proposed technique is preferable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here.

Keywords

Object Recognition Local Parametrisation Machine Intelligence Triangular Mesh Range Image 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P J Besl and R C Jain. Three dimentional object recognition. ACM Computing Surveys, 17:75–145, 1985.CrossRefGoogle Scholar
  2. [2]
    T W Chen and W C Lin. A neural network approach to csg-based 3-d object recognition. IEEE Trans. on Pattern Analysis and Machine Intelligence, 16(7):719–726, 1994.CrossRefGoogle Scholar
  3. [3]
    R T Chin and C R Dyer. Model-based recognition in robot vision. In ACM Computing Surveys, volume 18, pages 67–108, 1986.CrossRefGoogle Scholar
  4. [4]
    A Goetz. Introduction to differential geometry. Addison-Wesley, Reading, MA, 1970.zbMATHGoogle Scholar
  5. [5]
    A Hilton, A J Stoddart, J Illingworth, and T Windeatt. Marching triangles: Range image fusion for complex object modelling. In Proc IEEE International Conference on Image Processing, pages 381–384, Lausanne, Switzerland, 1996.Google Scholar
  6. [6]
    H Hoppe. Progressive meshes. In Proc SIGGRAPH, pages 99–106, 1996.Google Scholar
  7. [7]
    J J Koenderink. Solid shape. MIT Press, Cambridge, MA, 1990.Google Scholar
  8. [8]
    A K Mackworth and F Mokhtarian. Scale-based description of planar curves. In Proc Canadian Society for Computational Studies of Intelligence, pages 114–119, London, Ontario, 1984.Google Scholar
  9. [9]
    F Mokhtarian. A theory of multi-scale, torsion-based shape representation for space curves. Computer Vision and Image Understanding, 68(1):1–17, 1997.CrossRefMathSciNetGoogle Scholar
  10. [10]
    F Mokhtarian, N Khalili, and P Yuen. Multi-scale 3-d free-form surface smoothing. In Proc British Machine Vision Conference, pages 730–739, 1998.Google Scholar
  11. [11]
    F Mokhtarian and A K Mackworth. Scale-based description and recognition of planar curves and two-dimensional shapes. IEEE Trans Pattern Analysis and Machine Intelligence, 8(1):34–43, 1986.CrossRefGoogle Scholar
  12. [12]
    F Mokhtarian and A K Mackworth. A theory of multi-scale, curvature-based shape representation for planar curves. IEEE Trans Pattern Analysis and Machine Intelligence, 14(8):789–805, 1992.CrossRefGoogle Scholar
  13. [13]
    M Pilu and R Fisher. Recognition of geons by parametric deformable contour models. In Proc European Conference on Computer Vision, pages 71–82, Cambridge, UK, 1996.Google Scholar
  14. [14]
    H Samet. The design and analysis of spatial data structures. Addison-Wesley, 1990.Google Scholar
  15. [15]
    M Seibert and A M Waxman. Adaptive 3-d object recognition from multiple views. In IEEE Trans Pattern Analysis and Machine Intelligence, volume 14, pages 107–124, 1992.CrossRefGoogle Scholar
  16. [16]
    J A Sethian. Level set methods. Cambridge University Press, 1996.Google Scholar
  17. [17]
    S S Sinha and R Jain. Range image analysis. In Handbook of Pattern Recognition and Image Processing: Computer Vision (T Y Young, ed.), volume 2, pages 185–237, 1994.Google Scholar
  18. [18]
    F Solina and R Bajcsy. recovery of parametric models from range images: Thee case for superquadrics with global deformations. IEEE Trans. on Pattern Analysis and Machine intelligence, 12:131–147, 1990.CrossRefGoogle Scholar
  19. [19]
    B I Soroka and R K Bajcsy. Generalized cylinders from serial sections. In Proc IJCPR, 1976.Google Scholar
  20. [20]
    A J Stoddart and M Baker. Reconstruction of smooth surfaces with arbitrary topology adaptive splines. In Proc ECCV, 1998.Google Scholar
  21. [21]
    P Suetens, P Fua, and A J Hanson. Computational strategies for object recognition. ACM Computing Surveys, 24(2):5–61, 1992.CrossRefGoogle Scholar
  22. [22]
    G Taubin. Curve and surface smoothing without shrinkage. In Proc ICCV, pages 852–857, 1995.Google Scholar
  23. [23]
    G Taubin. Optimal surface smoothing as filter design. In Proc ECCV, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Nasser Khalili
    • 1
  • Farzin Mokhtarian
    • 1
  • Peter Yuen
    • 1
  1. 1.Centre for Vision, Speech, and Signal Processing Department of Electronic and Electrical EngineeringUniversity of SurreyGuildfordUK

Personalised recommendations