Surface Area Estimation of Digitized Planes Using Weighted Local Configurations

  • Joakim Lindblad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

We describe a method for estimating surface area of three-dimensional binary objects. The method assigns a surface area weight to each 2 × 2 × 2 configuration of voxels. The total surface area is given by a summation of the local area contributions for a digital object. We derive optimal area weights, in order to get an unbiased estimate with minimum variance for randomly oriented planar surfaces. This gives a coefficient of variation (CV) of 1.40% for planar regions. To verify the results and to address the feasibility for area estimation of curved surfaces, the method is tested on convex and non-convex synthetic test objects of increasing size. The algorithm is appealingly simple and uses only a small local neighbourhood. This allows efficient implementations in hardware and/or in parallel architectures.

Keywords

Surface area estimation marching cubes optimal weights digital planes local voxel configurations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Coeurjolly, D., Flin, F., Teytaud, O., Tougne, L.: Multigrid convergence and surface area estimation. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging. LNCS, vol. 2616, pp. 101–119. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Coeurjolly, D., Klette, R.: A comparative evaluation of length estimators. In: Proceedings of the 16th International Conference on Pattern Recognition (ICPR), pages IV, pp. 330–334. IEEE Computer Science, Los Alamitos (2002)Google Scholar
  3. 3.
    Dorst, L., Smeulders, A.W.M.: Length estimators for digitized contours. Computer Vision, Graphics and Image Processing 40, 311–333 (1987)CrossRefGoogle Scholar
  4. 4.
    Freeman, H.: Boundary encoding and processing. In: Lipkin, B.S., Rosenfeld, A. (eds.) Picture Processing and Psychopictorics, pp. 241–266. Academic Press, London (1970)Google Scholar
  5. 5.
    Kenmochi, Y., Klette, R.: Surface area estimation for digitized regular solids. In: Latecki, L.J., Melter, R.A., Mount, D.M., Wu, A.Y. (eds.) Vision Geometry IX. Proc. SPIE, vol. 4117, pp. 100–111 (2000)Google Scholar
  6. 6.
    Klette, R.: Multigrid convergence of geometric features. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 314–333. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Klette, R., Sun, H.J.: Digital planar segment based polyhedrization for surface area estimation. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 356–366. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Kulpa, Z.: Area and perimeter measurement of blobs in discrete binary pictures. Computer Graphics and Image Processing 6, 434–454 (1977)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lindblad, J., Nyström, I.: Surface area estimation of digitized 3D objects using local computations. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 267–278. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Lorensen, W.E., Cline, H.E.: Marching Cubes: A high resolution 3D surface construction algorithm. In: Proceedings of the 14th ACM SIGGRAPH on Computer Graphics, vol. 21, pp. 163–169 (1987)Google Scholar
  11. 11.
    Mullikin, J.C., Verbeek, P.W.: Surface area estimation of digitized planes. Bioimaging 1(1), 6–16 (1993)CrossRefGoogle Scholar
  12. 12.
    Proffit, D., Rosen, D.: Metrication errors and coding efficiency of chain-encoding schemes for the representation of lines and edges. Computer Graphics and Image Processing 10, 318–332 (1979)CrossRefGoogle Scholar
  13. 13.
    Young, I.T.: Sampling density and quantitative microscopy. Analytical and Quantitative Cytology and Histology 10(4), 269–275 (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Joakim Lindblad
    • 1
  1. 1.Centre for Image AnalysisUppsala UniversityUppsalaSweden

Personalised recommendations