Skip to main content
SpringerLink
Log in

Recent developments in the stereological analysis of particles

  • Stereology
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Recent developments in the stereological analysis of particles are reviewed. The trend has been towards methods which are applicable without specific assumptions about particle shape. Geometric samples of a local 3-d character are used. Stereological estimators of particle intensity, particle size distribution and particle interaction are presented and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Coleman, R. (1989). Inverse problems, Journal of Microscopy, 153, 233–248.

    Google Scholar 

  • Cruz-Orive, L. M. (1980). On the estimation of particle number, Journal of Microscopy, 120, 15–27.

    Google Scholar 

  • Cruz-Orive, L. M. (1987a). Stereology: recent solutions to old problems and a glimpse into the future, Acta Stereologica, 6, 3–18.5.

    Google Scholar 

  • Cruz-Orive, L. M. (1987b). Particle number can be estimated using a disector of unknowm thickness: The selector, Journal of Microscopy, 145, 121–142.

    Google Scholar 

  • Cruz-Orive, L. M. (1989). Second-order stereology: Estimation of second moment volume measres, Acta Stereologica, 8, 641–646.

    Google Scholar 

  • Evans, S. M. and Gundersen, H. J. G. (1989). Estimation of spatial distributions using the nucleator, Acta Stereologica, 8, 395–400.

    Google Scholar 

  • Federer, H. (1969). Geometric Measure Theory, Springer, Berlin.

    Google Scholar 

  • Gundersen, H. J. G. (1977). Notes on the estimation of the numerical density of arbitrary profiles: The edge effect, Journal of Microscopy, 111, 219–223.

    Google Scholar 

  • Gundersen, H. J. G. (1978). Estimators of the number of objects per unit area unbiased by edge effects, Microscopica Acta, 81, 107–117.

    Google Scholar 

  • Gundersen, H. J. G. (1986). Stereology of arbitrary particles: A review of unbiased number and size estimators and the presentation of some new ones (in memory of William R. Thompson), Journal of Microscopy, 143, 3–45.

    Google Scholar 

  • Gundersen, H. J. G. (1988). The nucleator, Journal of Microscopy, 151, 3–21.

    Google Scholar 

  • Gundersen, H. J. G., Bendtsen, T. F., Korbo, L., Marcussen, N., Møller, A., Nielse, K., Nyengaard, J. R., Pakkenberg, B., Sørensen, F. B., Vesterby, A. and West, M. J. (1988a). Some new, simple and efficient stereological methods and their use in pathological research and diagnosis, Acta Pathologica Microbiologica et Immunologica Scandinavica, 96, 379–394.

    Google Scholar 

  • Gundersen, H. J. G., Bagger, P., Bendtsen, T. F., Evans, S. M., Korbo, L., Marcussen, N., Møller, A., Nielsen, K., Nyengaard, J. R., Pakkenberg, B., Sørensen, F. B., Vesterby, A. and West, M. J. (1988b). The new stereological tools: Disector, fractionator, nucleator and point sampled intercepts and their use in pathological research and diagnosis, Acta Pathologica Microbiologica et Immunologica Scandinavia, 96, 857–881.

    Google Scholar 

  • Hanisch, K.-H. (1981). On classes of random sets and point processes, Serdica, 7, 160–166.

    Google Scholar 

  • Hanisch, K.-H. (1983). On stereological estimation of second-order characteristics and of hardcore distances of systems of sphere-centres, Biometrical J., 25, 731–743.

    Google Scholar 

  • Hanisch, K.-H. and Stoyan, D. (1981). Stereological estimation of the radial distribution function of centres of spheres, Journal of Microscopy, 122, 131–141.

    Google Scholar 

  • Howard, V., Reid, S., Baddeley, A. and Boyde, A. (1985). Unbiased estimation of particle density in the tanden scanning reflected light microscope, Journal of Microscopy, 138, 203–212.

    Google Scholar 

  • Jensen, E. B. and Gundersen, H. J. G. (1985). The stereological estimation of moments of particle volume, J. Appl. Probab., 22, 82–98.

    Google Scholar 

  • Jensen, E. B. and Gundersen, H. J. G. (1987). Stereological estimation of surface area of arbitrary particles, Acta Stereologica, 6, 25–30.

    Google Scholar 

  • Jensen, E. B. and Gundersen, H. J. G. (1989). Fundamental stereological formulae based on isotropically orientated probes through fixed points with applications to particle analysis, Journal of Microscopy, 153, 249–267.

    Google Scholar 

  • Jensen, E. B. and Kiêu, K. (1991). A new integral geometric formula of Blaschke-Petkantschin type, Research report, No. 180, Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus (submitted to Math. Nachr.).

  • Jensen, E. B., Kiêu, K. and Gundersen, H. J. G. (1990a). On the stereological estimation of reduced moment measures, Ann. Inst. Statist. Math., 42, 445–461.

    Google Scholar 

  • Jensen, E. B., Kiêu, K. and Gundersen, H. J. G. (1990b). Second-order stereology, Acta Stereologica, 9, 15–35.

    Google Scholar 

  • Marcussen, N., Ottosen, P. D., Christensen, S. and Olsen, T. S. (1989). Atubular glomeruli in lithium-induced cronic nephropathy in rats, Laboratory Investioation, 61, 295–302.

    Google Scholar 

  • Matheron, G. (1975). Random Sets and Integral Geometry, Wiley, New York.

    Google Scholar 

  • Nielsen, K., Ørntoft, T. and Wolf, H. (1989). Stereologic estimates of the nuclear volume in noninvasive bladder tumors (Ta) correlated with the recurrence pattern, Cancer, 64, 2269–2274.

    Google Scholar 

  • Penttinen, A. and Stoyan, D. (1989). Statistical analysis for a class of line segment processes, Scand. J. Statist., 16, 153–168.

    Google Scholar 

  • Petran, M., Hadravsky, M., Egger, M. D. and Galambos, R. (1968). Tandem scanning reflected light microscope, J.tJ. Opt. Soc. Amer. A, 58, 661–664.

    Google Scholar 

  • Sterio, D. C. (1984). The unbiased estimation of number and sizes of arbitrary particles using the disector, Journal of Microscopy, 134, 127–136.

    Google Scholar 

  • Stoyan, D. (1984a). On correlations of marked point precesses, Math. Nachr., 116, 197–207.

    Google Scholar 

  • Stoyan, D. (1984b). Further stereological formulae for spatial fibre processes, Mathematische Operationsforschung und Statistik, Series Statistics, 15, 421–428.

    Google Scholar 

  • Stoyan, D. (1985). Stereological determination of orientations, second-order quantities and correlations for random fibre systems, Biometrical J., 27, 411–425.

    Google Scholar 

  • Stoyan, D., Kendall, W. S. and Mecke, J. (1987). Stochastic Geometry and Its Applications, Akademie, Berlin.

    Google Scholar 

  • Tanemura, M. (1986). On the stereology of the radial distribution function of hard-sphere systems, Science of Form: Proceedings of the First International Symposium for Science on Form (eds. Y. Kato, R. Takaki and J. Toriwaki), 157–165, KTK Scientific Publishers, Tokyo.

    Google Scholar 

  • Watson, G. S. (1971). Estimating functionals of particle size distributions, Biometrika, 58, 483–490.

    Google Scholar 

  • Weibel, E. R. (1989). Measuring through the microscope: Development and evolution of stereological methods, Journal of Microscopy, 155, 393–403.

    Google Scholar 

  • Wicksell, S. D. (1925). The corpuscle problem I, Biometrika, 17, 84–89.

    Google Scholar 

  • Wicksell, S. D. (1926). The corpuscle problem II, Biometrika, 18, 152–172.

    Google Scholar 

  • Zähle, M. (1990). A kinematic formula and moment measures of random sets, Math. Nachr., 149, 325–340.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, Ny Munkegade, DK-8000, Aarhus C, Denmark

    Eva B. Vedel Jensen

Authors
  1. Eva B. Vedel Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

An earlier version of this article was presented at the Symposium on the Analysis of Statistical Information held in the Institute of Statistical Mathematics, Tokyo during December 5–8, 1989.

About this article

Cite this article

Vedel Jensen, E.B. Recent developments in the stereological analysis of particles. Ann Inst Stat Math 43, 455–468 (1991). https://doi.org/10.1007/BF00053366

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00053366

Key words and phrases

Search

Navigation