Decomposition in stereological unfolding problems

Viktor Beneš; Pavel Krejčíř

Kybernetika (1997)

  • Volume: 33, Issue: 3, page 245-258
  • ISSN: 0023-5954

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Beneš, Viktor, and Krejčíř, Pavel. "Decomposition in stereological unfolding problems." Kybernetika 33.3 (1997): 245-258. <http://eudml.org/doc/27866>.

@article{Beneš1997,
author = {Beneš, Viktor, Krejčíř, Pavel},
journal = {Kybernetika},
keywords = {stereological unfolding; particle systems; conditional independence; trivariate size-shape-orientation distribution},
language = {eng},
number = {3},
pages = {245-258},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Decomposition in stereological unfolding problems},
url = {http://eudml.org/doc/27866},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Beneš, Viktor
AU - Krejčíř, Pavel
TI - Decomposition in stereological unfolding problems
JO - Kybernetika
PY - 1997
PB - Institute of Information Theory and Automation AS CR
VL - 33
IS - 3
SP - 245
EP - 258
LA - eng
KW - stereological unfolding; particle systems; conditional independence; trivariate size-shape-orientation distribution
UR - http://eudml.org/doc/27866
ER -

References

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  2. V. Beneš A. M. Gokhale, M. Slámova, Unfolding the bivariate size-orientation distribution, Acta Stereol. 15, (1996), 1, 9-14. (1996) 
  3. R. Coleman, Inverse problems, J. Microsc. 153 (1989), 3, 233-248. (1989) 
  4. L. M. Cruz-Orive, Particle size-shape distributions: The general spheroid problem, I., II, J. Microsc. 107 (1976), 3, 235-253, 112 (1978), 153-167. (1976) 
  5. W. Gerlach, J. Ohser, On the accurancy of numerical solutions for some stereological problems as the Wicksell corpuscule problem, J. Biomath. 28 (1986), 7, 881-887. (1986) MR0872774
  6. A. M. Gokhale, Estimation of bivariate size and orientation distribution of microcracks, Acta Metall. and Mater. 44 (1996), 2, 475-485. (1996) 
  7. I. S. Gradshtejn, I. M. Ryzhik, Tables of Integrals, Sums, Series and Products, GIFML Moscow 1963. (In Russian.) (1963) 
  8. L. M. Karlsson, L. M. Cruz-Orive, The new stereological tools in metallography: estimation of pore size and number in aluminium, J. Microscopy 165 (1992), 3, 391-415. (1992) 
  9. A. Kleinwachter, M. Zähle, Size distribution stereology for quasiellipsoids in R n , Math. Oper. Stat. 17 (1986), 332-335. (1986) MR0849742
  10. P. Mikusinski H. Sherwood, M. D. Taylor, Probabilistic interpretations of copulas and their convex sums, In: Advances in Probability Distributions with Given Marginals (Dall'Aglio et al, eds.), Kluwer Acad. Publ., Dordrecht 1991, pp. 95-112. (1991) MR1215947
  11. J. Møller, Stereological analysis of particles of varying ellipsoidal shape, J. Appl. Probab. 25 (1988), 322-335. (1988) MR0938196
  12. J. Ohser, F. Mücklich, Stereology for some classes of polyhedrons, Adv. in Appl. Probab. 27 (1995), 2, 384-96. (1995) MR1334820
  13. B. W. Silvermann M. C. Jones D. W. Nychka, J. D. Wilson, A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography, J. Roy. Statist. Soc. Ser. B 52 (1990), 271-324. (1990) MR1064419
  14. C. van Putten, J. H. van Schuppen, Invariance properties of the conditional independence relation, Ann. Probab. 13 (1985), 3, 934-945. (1985) Zbl0576.60002MR0799429
  15. S. D. Wicksell, The corpuscule problem. A mathematical study of a biometrical problem, Biometrika 17 (1925), 84-88. (1925) 

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