Stereology of cubic particles: Various estimators for the size distribution

Journal of Microscopy

Volumn 187, Issue 1, 1997, Pages 22-30

  Ohser, J ^a   Nippe, M ^a  

^a TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

Particle systems; Planar sections; Size distribution; Stereology

Indexed keywords

CERMETS;

CUBIC PARTICLE; PARTICLE FORMS; PARTICLES SYSTEM; PLANAR SECTIONS; SECTION PROFILES; SIZE AND SHAPE; SIZE-DISTRIBUTION; SPATIAL SYSTEMS; STEREOLOGY; TRADITIONAL TECHNIQUES;

SIZE DISTRIBUTION;

CEMENT;

ALGORITHM; ARTICLE; HISTOGRAM; MICROSCOPE IMAGE; PARTICLE SIZE; PRIORITY JOURNAL; SCANNING ELECTRON MICROSCOPY; STATISTICAL ANALYSIS; STEREOLOGY;

EID: 0030808268     PISSN: 00222720     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-2818.1997.2020762.x     Document Type: Article

References (19)

1. Adrian, H. (1992) Statistical characteristics of selected polyhedra. Acta Stereol. 11, 143-155.
2. Berg, L. (1986) Lineare Gleichungssysteme mit Bandstruktur. VEB Deutscher Verlag der Wissenschaften, Berlin.
3. Bockstiegel, G. (1966) Eine einfache Formel zur Berechnung räumlicher Größenverteilungen aus durch Linearanalyse erhaltenen Daten. Z. Metallkde. 57, 647-656.
4. Gauthier, G., Quenec'h, J.-L., Coster, M. & Chermant, J.-L. (1994) Segmentation of grain boundaries in WC-Co cermets. Acta Stereol. 13, 203-208.
5. Gerlach, W. & Ohser, J. (1986) On the accuracy of numerical solutions such as the Wicksell corpuscle problem. Biometrical J. 28, 881-887.
6. Henrici, P. (1974) Applied and Computational Complex Analysis, Vol. 1. J. Wiley & Sons, New York.
7. Kanatani, K.I. (1985) Error analysis for the stereological estimation of sphere size distribution: Abel type integral equation. J. Comput. Phys. 57, 229-250.
8. Kneser, H. (1963) Schnitte durch Tetraeder. Proc. First Int. Congr. Stereol. (ed. by H. Hauk), 11/1-11/4. Ministry of Education, Vienna.
9. Myers, E.J. (1963) Sectioning of polyhedrons. Proc. First Int. Congr. Stereol. (ed. by H. Hauk), 15/1-15/6. Ministry of Education, Vienna.
10. Myers, E.J. (1967) Size distributions of cubic particles. Stereology, (ed. by H. Elias), pp. 187-188. Springer-Verlag, Berlin.
11. Ohser, J. & Mücklich, F. (1995) Stereology for some classes of polyhedrons. Adv. Appl. Prob. 27, 384-396.
12. Silverman, B.W., Jones, M.C., Nychka, D.W. & Wilson, J.D. (1990) A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography. J. R. Statist. Soc. B52, 271-324.
13. Socha, P. (1988) Random plane section of a polyhedron. Acta Stereol. 7, 41-46.
14. Stoyan, D., Kendall, W. S. & Mecke, J. (1995) Stochastic Geometry and its Applications, 2nd edn. J. Wiley & Sons, Chichester.
15. Sukiasian, G.S. (1982) On random section of polyhedra. Dokl. Akad. Nauk SSSR, 263, 809-812.
16. Voss, K. (1982) Frequencies of n-polygons in planar sections of polyhedra. J. Microsc. 128, 111-120.
17. Wicksell, S.D. (1925) The corpuscle problem I. Biometrika, 17, 84-89.
18. Wicksell, S.D. (1926) The corpuscle problem II. Biometrika, 18, 152-172.
19. Yosida (1980) Functional Analysis, 6th edn. Springer, Berlin.