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A World Where Mathematics And Microscopy Meet: Geometric Probability In Stereology Part Two

Posted in: Microscopy and Imaging
A World Where Mathematics And Microscopy Meet: Geometric Probability In Stereology Part Two

Following on from Part 1, we’ll now take a look at the actual use of geometric probability in stereology, as well as the advantages and disadvantages of this technique. As you’ll know from the introduction (here), stereology looks at the relativity between an object and its sections, while geometric probability allows a researcher to expand their data by providing additional information.

Layman’s terms

Geometric probability in stereology studies the relationship of the object, its sections and the factors that are independent of the objects’ structure and shape. In layman’s terms, stereology and geometric probability complement each other, as the former would not be complete without the latter.

Basic formula- it’s easy!

To obtain the quantities necessary to perform a stereological study using geometric probability, you can apply a simple formula, then simply plug in the known numbers so that you obtain the unknown measurements and then solve accordingly. The most basic formula to use is:

Ev (cvV)  =  Ea (caA)

Ev (V)          Ea (A)

‘V’ is the volume of the object.

‘A’ is the area of the object section.

‘cv’ is the volume composition of the object.

‘ca’ is the area composition of the object section.

The Ev signifies the average with respect to the object and the Ea refers to the average with regards to the object section.

Though there are other methods for conducting geometric probability in stereology, you can use this formula for just about any application, whether you are studying tissue samples, bone, mineral fragments or the brain.


Using geometric probability in stereology not only allows researchers to expand their data and perform a stereological study; it also provides unbiased results. The tools used to perform geometric probability allow for an accurate cell count and the grids help to identify outliers and determine proximity, all of which are beneficial when trying to figure out the relationship between specific objects and the space that surrounds them.


However, this does not mean the results are without bias, as geometric probability often relies on estimations. Still, the numbers do provide important information, such as the area of a tissue which has the most cell growth, or when and where antibody penetration is least likely to occur. Although the numbers may not be exact, they are still close enough to provide pertinent information that can help researchers analyse, learn, study, interpret and discover new details about people, the environment and other objects that play a key role in everyday living.

Get involved

This area of science and mathematics is very important to studying, analysing and diagnosing various specimens. If you intend on having a career that intertwines with this field, you should have a good understanding of the theories, methods, applications and interpretation of the results so you can get involved in the process.

See, we told you it wasn’t scary!

Overall, geometric probability in stereology is not as difficult a concept as you may have originally thought, especially once you break down the big, scary phrases into smaller pieces!

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Image Credit: David Cory

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