Stereological estimation of covariance using linear dipole probes

Journal of Microscopy

Volumn 195, Issue 2, 1999, Pages 96-103

  Reed, M G ^a   Howard, C V ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Covariance; Design based estimation; Dipole probes; Pair correlation function; Second order; Spatial arrangement; Vertical section; Volume

Indexed keywords

PROBES;

COVARIANCE; DESIGN BASED ESTIMATION; DIPOLE PROBES; LINEAR DIPOLES; PAIR CORRELATION FUNCTIONS; SECOND ORDERS; SPATIAL ARRANGEMENTS; STEREOLOGY; VERTICAL SECTION; VOLUME;

ANIMALS;

ARTICLE; COVARIANCE; DNA CONTENT; IMAGE ANALYSIS; LUNG VOLUME; PRIORITY JOURNAL; STATISTICAL ANALYSIS; STEREOLOGY; VOLUMETRY;

ANIMALIA;

EID: 0032775702     PISSN: 00222720     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-2818.1999.00592.x     Document Type: Article

References (32)

1. Baddeley, A.J. (1993) Stereology and survey sampling theory. Bull. Intern. Statist. Inst., Proc. 49th Session, Florence, 1993. 52 (2), 435-449.
2. Baddeley, A.J., Gundersen, H.J.G. & Cruz-Orive, L.M. (1986) Estimation of surface area from vertical sections. J. Microsc. 142, 259-276.
3. Baddeley, A.J., Howard, C.V., Boyde, A. & Reid, S. (1987) Three-dimensional analysis of the spatial distribution of particles using the tandem-scanning reflected light microscope. Acta Stereol. 6 (Suppl. II), 87-100.
4. Baddeley, A.J., Moyeed, R.A., Howard, C.V. & Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Appl. Statist. 42, 641-668.
5. Cressie, N.A.C. (1993) Statistics for Spatial Data (2nd edn). Wiley, Chichester.
6. Cruz-Orive, L.M. (1989) Second-order stereology: estimation of second moment, measures. Acta Stereol. 8, 641-646.
7. Cruz-Orive, L.M. & Hunziker, E.B. (1986) Stereology for anisotropic cells: application to growth cartilage. J. Microsc. 143, 47-80.
8. Delesse, M.A. (1847) Procédé mécanique pour déterminer la composition des roches. C.R. Acad. Sci. Paris. 25, 544-545.
9. Diggle, P.J. (1983) Statistical Analysis of Spatial Point Patterns. Academic Press, London.
10. Evans, S.M. & Gundersen, H.J.G. (1989) Estimation of spatial distributions using the nucleator. Acta Stereol. 8, 595-400.
11. Gerlach, W. & Stoyan, D. (1986) Determination of the covariance of random sets from thin sections. Biometr. J. 4, 427-132.
12. Getis, A. & Boots, B. (1978) Models of Spatial Processes. An Approach to the study of Points Lines and Area Patterns. Cambridge University Press, Cambridge.
13. Gundersen, H.J.G. & Østerby, R. (1981) Optimizing sampling efficiency of stereological studies in biology: or 'Do more less well!'. J. Microsc. 121, 65-73.
14. Jensen, E.B.V. & Kiêu, K. (1992) A note on recent research in second-order stereology, Acta Stereol. 11 (Suppl. I), 569-579.
15. Jensen, E.B., Kiêu, K. & Gundersen, H.J.G. (1990a) Second-order stereology. Acta Stereol. 9, 15-35.
16. Jensen, E.B., Kiêu, K. & Gundersen, H.J.G. (1990b) On the stereological estimation of reduced moment measures. Ann. Inst. Statist. Math. 42, 445-461.
17. Karlsson, L.M. & Liljeborg, A. (1994) Second-order stereology for pores in translucent alumina studied by confocal scanning laser microscopy. J. Microsc. 175, 186-194.
18. Kiêu, K. & Jensen, E.B.V. (1993) Stereological estimation based on isotropic slices through fixed points. J. Microsc. 170, 45-51.
19. König, D., Caravajal-Gonzales, S., Down, A.M., Vassy, J. & Rigaut, J.P. (1991) Modelling and analysis of 3-D arrangements of particles by point processes with examples of application to biological data obtained by confocal scanning light microscopy. J. Microsc. 161, 405-433.
20. Mattfeldt, T., Clarke, A. & Archenhold, G. (1994) Estimation of the directional distribution of spatial libre processes using stereology and confocal scanning laser microscopy. J. Microsc. 173, 87-101.
21. Mattfeldt, T., Frey, H. & Rose, C. (1995) Second-order stereology of benign and malignant alterations of the human mammary gland. J. Microsc. 171, 143-151.
22. Mattfeldt, T., Mall, G., Gharehbaghi, H. & Möller, P. (1990) Estimation of surface area and length with the orientator. J. Microsc. 159, 301-517.
23. Mattfeldt, T., Schmidt, V., Reepschläger, D., Rose, C. & Frey, H. (1996). Centred contact density functions for the statistical analysis of random sets. J. Microsc. 183, 158-169.
24. Miles, R.E. (1978) The importance of proper model specification in stereology. Geometrical Probability and Biological Structures: Buffons's 200th Anniversary. Lecture Notes in Biomathematics 23 (ed. by R. E. Miles and J. Serra), pp. 115-136. Springer-Verlag, Berlin.
25. 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.
26. Reed, M.G., Howard, C.V. & Shelton, C.G. (1997) Confocal imaging and second-order stereological analysis of a liquid foam. J. Microsc. 185, 313-320.
27. Ripley, B.D. (1981) Spatial Statistics. Wiley, New York.
28. Rosiwal, A. (1898) Ueber geometrische Gesteinsanalysen. Verh. K.K. Geol. Reichsant. Wien. 54, 11. (Cited in Weibel, E.R. (1979) Stereological Methods. Vol 1: Practical Methods for Biological Morphometry. Academic Press, London.)
29. Serra, J. (1982) Image Analysis and Mathematical Morphology Academic Press, London.
30. Stoyan, D., Kendall, W.S. & Mecke, J. (1995) Stochastic Geometry and its Applications (2nd edn). Wiley, Chichester.
31. Thompson, E. (1930) Quantitative microscopic analysis. J. Geol. 38, 193.
32. Torquato, S. (1998) Morphology and effective properties of disordered heterogenous media. Int. J. Solids Structures. 35, 2385.