Stereology is a branch of applied mathematics used for the three-dimensional analysis of organs and materials from two-dimensional measurements. Stereologic methods are versatile, easily understood, and simply applied. This paper provides anatomists with a practical guide to stereologic techniques and concepts and to ancillary morphometric methods. These methods allow investigators to calculate volume, surface, and numerical densities; make shape determinations; and calculate size distributions for spheres and rotatory ellipsoids. Other topics covered in this article include sampling methods, correction factors for shrinkage and section thickness, index of folding, automated and semiautomated image analysis, and three-dimensional reconstruction from serial sections.

An elementary introduction to stereology (quantitative microscopy).

Particle size distributions obtained from measurements in a thin section are usually a distorted version of the true distribution. When there is negligible overlap of images the conversion of the observed distribution involves the solution of a Volterra integral equation of the second kind. A closed form of solution is obtained for spherical particles, but it requires numerical integration. In practice a simple linear transformation of the frequencies in an observed histogram is more useful. The method is applied to delustrant and pigment particle sizes seen in a micrograph of a slice of polymer chip or extruded fibre.

http://iopscience.iop.org/article/10.1088/0508-3443/18/6/317/pdf

The calculation of true particle size distributions from the sizes observed in a thin slice

The size of grains and particles in metallic structures strongly influences many of the properties of the material. The kinetics of metallurgical processes, e.g. recrystallization, grain an...

Analysis of Grain- and Particle-Size Distributions in Metallic Materials

By means of stereological, i.e. statistico-geometrical methods the glomeruli of 8 human kidneys have been examined.

Stereology of the human renal glomerulus

Das Tomatensalatproblem (Bestimmung der Grosenverteilung von Kugeln aus der Grosenverteilung ihrer Schnittscheiben oder ebenen Schnittkreise) wird in groster Allgemeinheit gelost. Es werden Auswertungsverfahren und Formeln angegeben, die es erlauben, neben der Bestimmung von charakteristischen Grosen der Kugelverteilung (Anzahl der Kugeln pro Einheitsvolumen, Mittelwert der Radien, Streuung, mittleres Kugelvolumen usw.) auch die Haufigkeitsverteilung (Histogramm) der Kugeln auszurechnen.

Kugelgrößenverteilung und Verteilung der Schnittkreise; ihre wechselseitigen Beziehungen und Verfahren zur Bestimmung der einen aus der anderen

Es wird eine Methode angegeben, um die Anzahl der Kugeln im Einheitsvolumen und ihre Grosenordnung aus der nach links abbrechenden Verteilung der Schnittkreisradien zu bestimmen.

Über die Bestimmung von charakteristischen Größen einer Kugelverteilung aus der unvollständigen Verteilung der Schnittkreise

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Über die Bestimmung von charakteristischen Größen einer Kugelverteilung aus der unvollständigen Verteilung der Schnittkreise