This article is reproduced, with permission, from Lars Karlsson's website:
http://anatom1.unibe.ch/karlsson
Stereology is a spatial version of sampling theory.
Baddeley, A.J. Stereology. In: Spatial Statistics and Digital Image
Analysis, chapter 10, pp.181--216. National Research Council,
Washington DC, 1991.
Stereology originated as the problem of studying a three-dimensional physical
object from random two-dimensional plane sections or projections, and in
particular of estimating geometrical parameters such as volume, surface area,
length and total curvature.
Baddeley, A.J. Stereology and survey sampling theory. Bull. Intern.
Statis. Inst., Proceedings 49th Session,Florence 1993. 50
(2): 435--449, 1993.
Modern stereology can be regarded as sampling theory for spatial processes.
Baddeley, A.J. Stereology and survey sampling theory. Bull. Intern.
Statis. Inst., Proceedings 49th Session,Florence 1993. 50
(2): 435--449, 1993.
Stereology is a body of mathematical methods relating three-dimensional
parameters defining the structure to two-dimensional measurements obtainable on
sections of the structure.
Bertram, J.F. and Nurcombe, V. Counting cells with the new
stereology. Trends Cell. Biol. 2: 177--180, 1992.
A methodology for obtaining quantitative information of a geometric-statistical
nature from an object, using sections or projections of the object.
Cruz-Orive, L.M. Introduction to Stereology. Lecture Notes. Department
of Anatomy, University of Berne, 1988--89.
As a methodology: "Estimation of geometrical parameters of spatial structures
using properly sampled information". As a science: "A combination of
geometrical probability and statistics". As a liberal art: "Fun" (at least to
the author of these notes).
Cruz-Orive, L.M. Introduction to Stereology. Lecture Notes. Department
of Anatomy, University of Berne 1986--94.
Stereology is a very general collection of principles based on integral
geometry, probability theory and sampling theory, as opposed to "techniques" or
ad-hoc "methods". Stereology may therefore grow by the incorporation of new
principles but, like Euclid's Elements, stereology will be well alive after the
last scanning instrument, as we know it today, has fallen into oblivion.
Cruz-Orive, L.M. Discussion of topic IN22: Stereology. Bull. Intern.
Statis. Inst., Proceedings 49th Session, Florence 1993. 55(4):
162, 1993.
"Stereology", or the generalization of planar structure measurements to three
dimensions, ...
Harrigan, T.P. and Mann, R.W. Characterization of microstructural
anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci.
19: 761--767, 1984.
Stereology, a branch of applied geometric probability, concerns the
determination of internal geometric properties of a three-dimensional object
from lower-dimensional information such as that provided by a planar section
through the object.
Jensen, E.B. Design- and model-based stereological analysis of
arbitrarily shaped particles. Scand. J. Statist. 14: 161--180,
1987.
Stereological methods concern the estimation of quantitative properties of
spatial materials from lower-dimensional information such as that generated by
a section through the material.
Jensen, E.B. and Gundersen, H.J.G. The Stereological Estimation
of Moments of Particle Volume. J. Appl. Prob. 22: 82--98, 1985.
...in stereology, "applied geometrical probability", which show...
Jensen, E.B., Baddeley, A.J., Gundersen, H.J.G. and Sundberg,
R. Recent Trends in Stereology. Intern. Statist. Rev. 53:
99--108, 1985.
...stereology is sampling in three dimensions...
Karlsson, L.M. and Cruz-Orive, L.M. Estimation of Pore Size in
Aluminium using the Disector, the Selector and Cavalieri's Principle. MiCon 90:
Advances in Video Technology for Microstructural Control. ASTM STP 1094
(ed. G.F. Van der Voort), pp. 277--291. American Society for Testing and
Materials, Philadelphia, 1991.
Stereology is concerned with the estimation of meaningful quantities defined in
a three-dimensional (3-D) structure from measurements made in a proper sample
of the structure.
Karlsson, L.M. and Cruz-Orive, L.M. The New Stereological Tools
in Metallography: Estimation of Pore Size and Number in Aluminium. J. Microsc.
165: 391--415, 1992.
...stereology is sometimes regarded as "sampling theory for populations
exhibiting a geometrical structure."
Kubinova, L. Advantages of Stereological Methods in Biomedicine. IEEE
Engineering in Medicine and Biology March/April: 110--115,
1998.
... a topic in applied mathematics known as stereology.
Roberts, N., Barbosa, S., Blumhardt, L.D., Kawoski, R.A. and Edwards,
R.H.T. Stereological estimation of the total volume of MR visible brain
lesions in patients with multiple sclerosis. MAGMA 2: 375--378, 1994.
The objective of stereology is to draw inferences about the geometrical
properties of three-dimensional structures when information is only available
in some lower-dimensional form via linear probes, planar sections, or
projections of thin slices.
Stoyan, D., Kendall, W.S. and Mecke, J. Stochastic Geometry
and its Applications. J. Wiley & Sons, Chichester, 1995.
The science of stereology is dealing with the transformation of two-dimensional
observations to three-dimensional information, using mathematical, statistical,
and geometrical tools.
Vesterby, A. Star volume in bone research. A histomorphometric analysis
of trabecular bone structure using vertical sections. Anat. Rec. 235:
325--334, 1993.
At a practical level, stereological methods are precise tools for obtaining
quantitative information about three-dimensional structures based on sections.
Vesterby, A. Star volume in bone research. A histomorphometric analysis
of trabecular bone structure using vertical sections. Anat. Rec. 235:
325--334, 1993.
Stereology is a body of mathematical methods relating three-dimensional
parameters defining the structure to two-dimensional measurements obtainable on
sections of the structure.
Weibel, E.R. Stereological Methods, Vol. 1. Practical Methods for
Biological Morphometry. Academic Press, London , 1979.
Weibel, E.R. Stereological Methods, Vol. 2. Theoretical Fundations.
Academic Press, London, 1980.
...the word "Stereology" was invented to describe the set of methods that allow
a 3D interpretation of structures based on observations made on 2D sections.
Weibel, E.R. Stereology in perspective: a mature science evolves. Acta
Stereol. 11/Suppl. I: 1--13, 1992.
Stereology is a body of procedures, mainly geometrical-statistical, which have
in mind the aim of obtaining information about three-dimensional structures
from two-dimensional, flat images. It can also be defined as extrapolation from
two- to three-dimensional space.
Weibel, E.R. and Elias, H. Quantitative Methods in Morphology,
Springer, Berlin, 1967.