Fractional trend of the variance in cavalieri sampling

Image Analysis and Stereology

Volumn 19, Issue 2, 2000, Pages 71-79

  García Fiñana, Marta ^a   Cruz Orive, Luis M ^a  

^a UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Area function; Cavalieri estimator; Extension term; Fractional derivative; Fractional smoothness constant; Zitterbewegung

Indexed keywords

EID: 0002672657     PISSN: 15803139     EISSN: 18545165     Source Type: Journal    
DOI: 10.5566/ias.v19.p71-79     Document Type: Article

References (14)

1. Abramowitz M, Stegun IA (1965). Handbook of Mathematical Functions. New York: Dover.
2. Cruz-Orive LM (1999). Precision of Cavalieri sections and slices with local errors. J Microsc 193:182-98.
3. García-Fiñana M, Cruz-Orive LM (1998). Explanation of apparent paradoxes in Cavalieri sampling. Acta Stereol 17:293-302.
4. García-Fiñana M, Cruz-Orive LM (1999). New approximations for the efficiency of Cavalieri sampling. Internal report 3/99. University of Cantabria: Department of Mathematics. J Microsc, in press.
5. Gardner M (1978). Mathematical Carnival. Harmondsworth: Penguin.
6. Gundersen HJG, Jensen EB, Kiêu K, Nielsen J (1999). The efficiency of systematic sampling in stereology -reconsidered. J Microsc 193:199-211.
7. Kiêu K (1997). Three lectures on systematic geometric sampling. Memoirs 13/1997. University of Aarhus: Department of Theoretical Statistics.
8. Kiêu K, Souchet S, Istas J (1999). Precision of systematic sampling and transitive methods. J Statist Planning Inf 77:263-79.
9. Matheron G (1965). Les Variables Régionalisées et Leur Estimation. Paris: Masson et Cie.
10. Matheron G (1971). The Theory of Regionalized Variables and Its Applications. Les Cahiers du Centre de Morphologie Mathématique de Fontainebleau, No 5. Fontainebleau: école Nationale Supérieure des Mines de Paris.
11. McNulty V, Cruz-Orive LM, Roberts N, Holmes CJ, Gual-Arnau X (2000). Estimation of brain compartment volume from MR Cavalieri slices. J Comput Assist Tomogr, in press.
12. Nishimoto K (1984). Fractional Calculus. Koriyama: Descartes Press CO.
13. Roberts N, Garden AS, Cruz-Orive LM, Whitehouse GH, Edwards RHT (1994). Estimation of fetal volume by MRI and stereology. Br J Radiol 67:1067-77.
14. Souchet S (1995). Précision de l'estimateur de Cavalieri. Rapport de stage, D.E.A. de Statistiques et Modéles Aléatoires appliqués à la Finance. Université Paris-VII. INRA-Versailles: Laboratoire de Biométrie.