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Recent developments in the stereological analysis of particles. (English) Zbl 0850.60004

60D05 Geometric probability and stochastic geometry
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[1] Coleman, R. (1989). Inverse problems, Journal of Microscopy, 153, 233-248.
[2] Cruz-Orive, L. M. (1980). On the estimation of particle number, Journal of Microscopy, 120, 15-27.
[3] Cruz-Orive, L. M. (1987a). Stereology: recent solutions to old problems and a glimpse into the future, Acta Stereologica, 6, 3-18.5.
[4] Cruz-Orive, L. M. (1987b). Particle number can be estimated using a disector of unknowm thickness: The selector, Journal of Microscopy, 145, 121-142.
[5] Cruz-Orive, L. M. (1989). Second-order stereology: Estimation of second moment volume measres, Acta Stereologica, 8, 641-646.
[6] Evans, S. M. and Gundersen, H. J. G. (1989). Estimation of spatial distributions using the nucleator, Acta Stereologica, 8, 395-400.
[7] Federer, H. (1969). Geometric Measure Theory, Springer, Berlin. · Zbl 0176.00801
[8] 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.
[9] Gundersen, H. J. G. (1978). Estimators of the number of objects per unit area unbiased by edge effects, Microscopica Acta, 81, 107-117.
[10] 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.
[11] Gundersen, H. J. G. (1988). The nucleator, Journal of Microscopy, 151, 3-21.
[12] 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.
[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., 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.
[14] Hanisch, K.-H. (1981). On classes of random sets and point processes, Serdica, 7, 160-166. · Zbl 0493.60020
[15] 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. · Zbl 0567.60014
[16] Hanisch, K.-H. and Stoyan, D. (1981). Stereological estimation of the radial distribution function of centres of spheres, Journal of Microscopy, 122, 131-141.
[17] 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.
[18] Jensen, E. B. and Gundersen, H. J. G. (1985). The stereological estimation of moments of particle volume, J. Appl. Probab., 22, 82-98. · Zbl 0559.60013
[19] Jensen, E. B. and Gundersen, H. J. G. (1987). Stereological estimation of surface area of arbitrary particles, Acta Stereologica, 6, 25-30.
[20] 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.
[21] 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.). · Zbl 0784.53043
[22] 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. · Zbl 0724.60012
[23] Jensen, E. B., Kiêu, K. and Gundersen, H. J. G. (1990b). Second-order stereology, Acta Stereologica, 9, 15-35. · Zbl 0701.60008
[24] 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.
[25] Matheron, G. (1975). Random Sets and Integral Geometry, Wiley, New York. · Zbl 0321.60009
[26] 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.
[27] Penttinen, A. and Stoyan, D. (1989). Statistical analysis for a class of line segment processes, Scand. J. Statist., 16, 153-168. · Zbl 0688.62054
[28] 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.
[29] Sterio, D. C. (1984). The unbiased estimation of number and sizes of arbitrary particles using the disector, Journal of Microscopy, 134, 127-136.
[30] Stoyan, D. (1984a). On correlations of marked point precesses, Math. Nachr., 116, 197-207. · Zbl 0554.60055
[31] Stoyan, D. (1984b). Further stereological formulae for spatial fibre processes, Mathematische Operationsforschung und Statistik, Series Statistics, 15, 421-428. · Zbl 0547.60018
[32] Stoyan, D. (1985). Stereological determination of orientations, second-order quantities and correlations for random fibre systems, Biometrical J., 27, 411-425. · Zbl 0597.62099
[33] Stoyan, D., Kendall, W. S. and Mecke, J. (1987). Stochastic Geometry and Its Applications, Akademie, Berlin. · Zbl 0622.60019
[34] 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.
[35] Watson, G. S. (1971). Estimating functionals of particle size distributions, Biometrika, 58, 483-490. · Zbl 0228.62026
[36] Weibel, E. R. (1989). Measuring through the microscope: Development and evolution of stereological methods, Journal of Microscopy, 155, 393-403.
[37] Wicksell, S. D. (1925). The corpuscle problem I, Biometrika, 17, 84-89. · JFM 51.0392.02
[38] Wicksell, S. D. (1926). The corpuscle problem II, Biometrika, 18, 152-172. · JFM 52.0528.03
[39] Zähle, M. (1990). A kinematic formula and moment measures of random sets, Math. Nachr., 149, 325-340. · Zbl 0725.60014
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