A Comparison of Digital Length Estimators for Image Features

  • V. Toh
  • C. A. Glasbey
  • A. J. Gray
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2749)

Abstract

Image analysis methods for estimating size of object features extract pixel-based measurements, after object segmentation, then convert these to an estimate of actual size; e.g. segmentation of a cell in a randomly located 2-D cross-sectional image, counting no. of pixels on the cell boundary, and converting to an estimate of cell surface area using geometrical formulae. Stereology takes a quite different approach to estimating higher dimensional properties of an object, by using a randomly orientated 2-D specimen section or 2-D projection of a 3-D object. Geometrical properties and sampling theory enable inference of 3-D properties; e.g. feature length is estimated by counting intersections with a randomly superimposed test grid with fixed known spacing. This work compares these two approaches for image feature length estimation, using a simulation study. We generate binary straight line structures and planar curves of known size and compare results from several different estimators of feature length, including a novel estimator which weights pixel count by estimating local curve orientation.

Keywords

Stereological Method Stereological Estimation Mouse Mammary Tissue Stereological Approach Walk Curve 
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.

References

  1. 1.
    Baddeley, A.: Stochastic Geometry: An introduction and reading-list. International Statistical Review 50 (1982) 179–193MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Buffon, G.L.L. Comte de.: Essai d’Arithmetique Morale. In Supplement a l’Histoire Naturelle, Volume 4 Imprimerie Royale, Paris (1777)Google Scholar
  3. 3.
    Dorst, L. and Smeulders, A.W.M.: Length estimators for digitized contours. Computer Vision, Graphics and Image Processing 40 (1987) 311–333CrossRefGoogle Scholar
  4. 4.
    Freeman, H.: Boundary encoding and processing. In B.S. Lipkin and A. Rosenfeld (Eds.), Picture Processing and Psychopictorics. Academic Press, New York (1970) 241–266Google Scholar
  5. 5.
    Freeman, H.: Computer processing of line-drawing images. Computing Surveys 6 (1974) 57–97MATHCrossRefGoogle Scholar
  6. 6.
    Glasbey, C.A. and Horgan, G.W.: Image Analysis for the Biological Sciences. Wiley, Chichester (1995)MATHGoogle Scholar
  7. 7.
    Howard, C.V. and Reed, M.G.: Unbiased Stereology: Three-dimensional Measurement in Microscopy. BIOS Scientific, Oxford (1998)Google Scholar
  8. 8.
    Kulpa, Z.: Area and perimeter measurement of blobs in discrete binary pictures. Computer Graphics and Image Processing 6 (1977) 434–451MathSciNetCrossRefGoogle Scholar
  9. 9.
    Vossepoel, A.M. and Smeulders, A.W.M.: Vector code probability and metrication error in the representation of straight lines of finite length. Computer Graphics and Image Processing 20, (1982) 347–64.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • V. Toh
    • 1
  • C. A. Glasbey
    • 2
  • A. J. Gray
    • 1
  1. 1.Department of Statistics and Modelling ScienceUniversity of StrathclydeGlasgowUK
  2. 2.Biomathematics and Statistics ScotlandEdinburghUK

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