Edge-corrected estimators of the nearest-neighbour distance distribution function for three-dimensional point patterns

Journal of Microscopy

Volumn 186, Issue 2, 1997, Pages 177-184

  Reed, M G ^a   Howard, C V ^b  

^a SHELL RESEARCH AND TECHNOLOGY CENTRE   (Netherlands)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Edge effect; nearest neighbour distance distribution function; point processes; second order stereology; spatial statistics; stochastic geometry

Indexed keywords

DISTRIBUTION FUNCTIONS; EMBEDDED SYSTEMS; INTELLIGENT SYSTEMS; MATRIX ALGEBRA; MONTE CARLO METHODS; SPATIAL DISTRIBUTION; STATISTICS; STOCHASTIC SYSTEMS;

DISTANCE DISTRIBUTION FUNCTIONS; EDGE-EFFECTS; NEAR-NEIGHBOR DISTANCE DISTRIBUTION FUNCTION; NEAREST NEIGHBOR DISTANCE; POINT PROCESS; SECOND ORDERS; SECOND-ORDER STEREOLOGY; SPATIAL STATISTICS; STEREOLOGY; STOCHASTIC GEOMETRY;

BRICK;

ARTICLE; PRIORITY JOURNAL; RANDOMIZATION; SAMPLE; SPATIAL DISCRIMINATION; STEREOLOGY; THREE DIMENSIONAL IMAGING;

EID: 0030991898     PISSN: 00222720     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-2818.1997.1710741.x     Document Type: Article

References (25)

1. Baddeley, A.J. & Gill, R.D. (1993) Kaplan-Meier estimators of Interpoint distance distributions for spatial point processes. CWI Research report BS-R9315, CWI Amsterdam.
2. 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.
3. 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.
4. Chiu, S.N. & Stoyan, D. (1996) Estimators of distance distributions for spatial patterns. Statistica Neerlandica, in press.
5. Cochran, W.G. (1951) Sampling Techniques. Wiley, New York.
6. Cressie, N.A.C. (1993) Statistics for Spatial Data, 2nd edn. Wiley, Chichester.
7. Cruz-Orive, L.M. (1980) Best linear unbiased estimators for stereology. Biometrics, 36, 595-605.
8. Cruz-Orive, L.M. (1989) Second-order stereology: estimation of second moment volume measures. Acta Stereol. 8, 641-646.
9. Diggle, P.J. (1983) Statistical Analysis of Spatial Point Patterns. Academic Press, London.
10. Doguwa, S.I. & Upton, G.J.G. (1990) On the estimation of the nearest neighbour distribution, G (t), for point processes. Biomed. J. 32, 863-876.
11. Floresroux, E.M. & Stein, M.L. (1996) A new method of edge correction for estimating the nearest neighbour distribution. J. Statist. Plann. Inf. (cited in Stoyan et al., 1995, p. 141).
12. Gundersen, H.J.G. (1977) Notes on the estimation of the numerical density of arbitrary profiles: the edge effect. J. Microsc. 111, 219-223.
13. 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., Sorensen, F.B., Vesterby, A. & West, M.J. (1988a) The new stereological tools: director, fractionator and point sampled intercepts and their use in pathological research. Acta Pathol. Microbiol. Immunol. Scand. 96, 857-881.
14. Gundersen, H.J.G., Bendtsen, T.F., Korbo, L., Marcussen, N., Møller, A., Nielsen, K., Nyengaard, J.R., Pakkenberg, B., Sorensen, F.B., Vesterby, A. & West, M.J. (1988b) Some new simple and efficient stereological methods and their use in pathological research and diagnosis. Acta Pathol. Microbiol. Immunol. Scand. 96, 379-394.
15. Hanisch, K.H. (1984) Some remarks on estimators of the distribution function of nearest neighbour distance in stationary spatial point patterns. Math. Oberforsch. Statist. Ser. Statist. 15, 409-412.
16. Howard, C.V., Reid, S., Baddeley, A. & Boyde, A. (1985) Unbiased estimation of particle density in the tandem scanning reflected light microscope. J. Microsc. 138, 203-212.
17. Jensen, E.B., Kièu, K. & Gundersen, H.J.G. (1990) Second-order stereology. Acta Stereol. 9, 15-35.
18. 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.
19. König, D., Carvajal-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., Frey, H. & Rose, C. (1993) Second-order stereology of benign and malignant alterations of the human mammary gland. J. Microsc. 171, 143-151.
21. Miles, R.E. (1974) On the elimination of edge effects in planar sampling. Stochastic Geometry (ed. by E. F. Harding and D. G. Kendall), pp. 228-247. Wiley, Chichester.
22. Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T. (1990) Numerical Recipes in C-The Art of Scientific Computing. Cambridge University Press.
23. Ripley, B.D. (1981) Spatial Statistics. Wiley, New York.
24. Ripley, B.D. (1988) Statistical Inference for Spatial Processes. Cambridge University Press, Cambridge.
25. Stoyan, D., Kendall, W.S. & Mecke, J. (1995) Stochastic Geometry and Its Applications, 2nd edn. Wiley, Chichester.