A new stereological principle for test lines in three-dimensional space

Journal of Microscopy

Volumn 219, Issue 1, 2005, Pages 18-28

  Cruz Orive, L M ^a  

^a UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Convex body; Crofton formulae; Integral geometry; Invariant probe; Particle; Pivotal point; Pivotal section; Platelet; Point sampled test line; Stereology; Support function; Support set; Surface area; Volume; Weighted mean

Indexed keywords

CONVEX BODY; CROFTON FORMULA; INTEGRAL GEOMETRY; INVARIANT PROBE; PARTICLE; PIVOTAL POINT; PIVOTAL SECTION; POINT-SAMPLED TEST LINE; STEREOLOGY; SUPPORT FUNCTIONS; SUPPORT SET; SURFACE AREA; TEST-LINES; VOLUME; WEIGHTED MEAN;

ARTICLE; GEOMETRY; PARTICLE SIZE; PRIORITY JOURNAL; SAMPLING; SPACE; STEREOLOGY; SURFACE PROPERTY; THICKNESS; THREE DIMENSIONAL IMAGING; VOLUMETRY;

EID: 22844438106     PISSN: 00222720     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1365-2818.2005.01489.x     Document Type: Article

References (26)

1. Baddeley, A.J., Gundersen, H.J.G. & Cruz-Orive, L.M. (1986) Estimation of surface area from vertical sections. J. Microsc. 142, 259-276.
2. Baddeley, A.J. & Jensen, E.B.V. (2004) Stereology for Statisticians. Chapman & Hall/CRC, London.
3. Cruz-Orive, L.M. (1987) Particle number can be estimated using a disector of unknown thickness: the selector. J. Microsc. 145, 121-142.
4. Cruz-Orive, L.M. (1989) Second-order stereology: estimation of second moment volume measures. Proc. ECS V Freiburg 1989. Acta Stereol. 8/ 2, 641-646.
5. Gardner, R.J. (1995) Geometric Tomography. Cambridge University Press, Cambridge.
6. Gittes, F. (1990) Estimating mean particle volume and number from random sections by sampling profile boundaries. J. Microsc. 158, 1-18.
7. Gundersen, H.J.G. (1988) The nucleator. J. Microsc. 151, 3-21.
8. Gundersen, H.J.G., Bagger, P., Bendtsen, S.M., Evans, T.F., Korbo, L., Marcussen, N., Møller, A., Nielsen, K., Nyengaard, J.R., Pakkenberg, B., Sørensen, F.B., Vesterby, A. & West, M.J. (1988) The new stereological tools: Disector, fractionator, nucleator and point sampled intercepts and their use in pathological research and diagnosis. APMIS, 96, 857-881.
9. Howard, C.V. & Reed, M.G. (2005) Unbiased Stereology. Three-dimensional Measurement in Microscopy, 2nd edn. Garland Science/BIOS Scientific Publishers, Abingdon, U.K.
10. Jensen, E.B.V. (1998) Local Stereology, World Scientific, Singapore.
11. Jensen, E.B. & Gundersen, H.J.G. (1985) The stereological estimation of moments of particle volume. J. Appl. Probab. 22, 82-98.
12. Jensen, E.B. & Gundersen, H.J.G. (1987) Stereological estimation of surface area of arbitrary particles. Acta Stereol. 6, 25-30.
13. Jensen, E.B. & Gundersen, H.J.G. (1989) Fundamental stereological formulae based on isotropically orientated probes through fixed points with applications to particle analysis. J. Microsc. 153, 249-267.
14. Jensen, E.B., Kiêu, K. & Gundersen, H.J.G. (1990) Second-order stereology. Proc. ECS V Freiburg 1989. Acta Stereol. 9/1, 15-35.
15. Karlsson, L.M. & Cruz-Orive, L.M. (1997) Estimation of mean particle size from single sections. J. Microsc. 186, 121-132.
16. Kiêu, K. & Jensen, E.B.V. (1993) Stereological estimation based on isotropic slices through fixed points. J. Microsc. 170, 45-51.
17. Mattfeldt, T., Mall, G., Gharehbaghi, H. & Möller, P. (1990) Estimation of surface area and length with the orientator. J. Microsc. 159, 301-317.
18. Miles, R.E. & Davy, P.J. (1976) Precise and general conditions for the validity of a comprehensive set of stereological fundamental formulae. J. Microsc. 107, 211-226.
19. Nyengaard, J.R. & Gundersen, H.J.G. (1992) The isector: a simple and direct method for generating isotropic, uniform random sections from small specimens. J. Microsc. 165, 427-431.
20. Ripley, B.D. (1981) Spatial Statistics. J. Wiley & Sons, New York.
21. Santaló, L.A. (1976) Integral Geometry and Geometrical Probability. Addison-Wesley, Reading, MA.
22. Sterio, D.C. (1984) The unbiased estimation of number and sizes of arbitrary particles using the disector. J. Microsc. 134, 127-136.
23. Stoyan, D., Kendall, W.S. & Mecke, J. (1995) Stochastic Geometry and its Applications, 2nd edn. J. Wiley & Sons, Chichester.
24. Varga, O. (1935) Integraleometrie 3. Croftons Formeln für den Raum. Math. Zeitschrift. 40, 387-405.
25. Weibel, E.R. (1979) Stereological Methods. Vol. 1: Practical Methods for Biological Morphometry. Academic Press, London.
26. West, M.J., Slomianka, L. & Gundersen, H.J.G. (1991) Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the optical fractionator. Anat. Rec. 231, 482-497.