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Surface Area Estimation in Practice

  • Guy Windreich
  • Nahum Kiryati
  • Gabriele Lohmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

Consider a complex, convoluted three dimensional object that has been digitized and is available as a set of voxels. We describe a fast, practical scheme for delineating a region of interest on the surface of the object and estimating its original area. The voxel representation is maintained and no triangulation is carried out. The methods presented rely on a theoretical result of Mullikin and Verbeek, and bridge the gap between their idealized setting and the harsh reality of 3D medical data. Performance evaluation results are provided, and operation on segmented white matter MR brain data is demonstrated.

Keywords

Surface area estimation digital geometry voxels objects morphometric measurements segmented white matter 

References

  1. 1.
    Artzy, E., Frieder, G., Herman, G.T.: The Theory, Design, Implementation and Evaluation of a Three-Dimensional Surface Detection Algorithm. Computer Graphics and Image Processing 1, 1–24 (1981)CrossRefGoogle Scholar
  2. 2.
    Couerjolly, D., Flin, F., Teytaud, O.: Digital Surface Area Estimation., abstract, in Dagstuhl Seminar Report no. 339, Schloss Dagstuhl, Germany (2002)Google Scholar
  3. 3.
    Dorst, L., Smeulders, A.W.M.: Length Estimators for Digital Contours. Computer Vision Graphics Image Processing 40, 311–333 (1987)CrossRefGoogle Scholar
  4. 4.
    Hahn, U., Sandau, K.: Precision of Surface Area Estimation Using Spatial Grids. Acta Stereologica 8, 425–430 (1989)Google Scholar
  5. 5.
    Koplowitz, J., Bruckstein, A.M.: Design of Perimeter Estimators for Digitized Planar Shapes. IEEE Trans. Pattern Analysis Machine Intelligence 11, 611–622 (1989)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Kenmochi, Y., Klette, R.: Surface Area Estimation for Digital Regular Solids., Technical Report CITR-TR-62, Computer Science Department, University of Auckland, New Zealand, Available online (2000)Google Scholar
  8. 8.
    Kimmel, R., Sethian, J.: Computing Geodesics on Manifolds. Proc. National Academy of Sciences 95, 8431–8435 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kiryati, N., Székely, G.: Estimating Shortest Paths and Minimal Distances on Digitized Three-Dimensional Surfaces. Pattern Recognition 26, 1623–1637 (1993)CrossRefGoogle Scholar
  10. 10.
    Klette, R., Wu, F., Zhou, S.: Multigrid Convergence of Surface Approximations., Technical Report CITR-TR-25, Computer Science Department, University of Auckland, New Zealand, Available online (1998)Google Scholar
  11. 11.
    Klette, R., Sun, H.J.: A Global Surface Area Estimation Algorithm for Digital Regular Solids., Technical Report CITR-TR-69, Computer Science Department, University of Auckland, New Zealand, Available online (2000)Google Scholar
  12. 12.
    Lohmann, G.: Volumetric Image Analysis. Wiley, Chichester/Teubner, Stuttgart (1998)zbMATHGoogle Scholar
  13. 13.
    Lorensen, W.E., Cline, H.E.: Marching Cubes: A High Resolution 3D Surface Construction Algorithm. ACM Computer Graphics 21, 163–169 (1987)CrossRefGoogle Scholar
  14. 14.
    Mullikin, J.C., Verbeek, P.W.: Surface Area Estimation of Digitized Planes. Bioimaging 1, 6–16 (1993)CrossRefGoogle Scholar
  15. 15.
    Zeng, X., Staib, L.H., Schultz, R.T., Duncan, J.S.: Segmentation and Measurement of the Cortex from 3-D MR Images Using Coupled-Surfaces Propagation. IEEE Transactions on Medical Imaging 18, 927–937 (1999)CrossRefGoogle Scholar
  16. 16.
    Windreich, G., Kiryati, N.: Voxel-based Surface Area Estimation., abstract, in Dagstuhl Seminar Report no. 339, Schloss Dagstuhl, Germany (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Guy Windreich
    • 1
  • Nahum Kiryati
    • 1
  • Gabriele Lohmann
    • 2
  1. 1.Dept. of Electrical Engineering–SystemsTel Aviv UniversityTel AvivIsrael
  2. 2.Max-Planck Institute of Cognitive NeuroscienceLeipzigGermany

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