A Brief Introduction to Stereology

Yuxiong (Max) Mao

Center for Advanced Vehicular System

Mississippi State University

Overview

What is stereology?

Stereological methods

Potential problems

– Inappropriate sampling

– Biased counting method

Automatic Measurements using ImageJ

Summary

What is Stereology?

“Stereo” is derived from the Greek word for a “geometric object”.

Think about your stereo set at home or stereo images. They are not called "stereo" because there are two speakers or two pictures, but because they try to recreate sounds or objects in there dimensional (3-D) space.

Stereology is the science of trying to recreate or estimate the properties of geometrical objects in 3-D space.

What are Properties of Objects in Space?

Space has three dimensions, and objects within it have properties for each possible number of dimensions.

Objects have– a volume (3 dimensions)

– a surface (2 dimensions)

– a length (1 dimension)

– a number (0 dimensions)

Each of these properties can be estimated by stereological methods.

2-D Sectioning Planes

Sectioning features in a 3-D space with a plane

– Area intersection with a volume (red),

– Line intersection with a surface (blue)

– Point intersection with a linear feature (green).

Measuring directly in 3-D space is generally not practical because most material microstructures are opaque.

The measurements are usually made on 2-D sections.

Stereological Methods The microstructure is measured by sampling it

with stereological probes.

The most common stereological probes are points, lines, surfaces and volumes.

Example : estimation of volume using points

The grid spacing is 1/2 cm and 10 points fall on the red area, so the estimated area is 10x(0.5)2 = 2.5cm2.

Stereological Methods - Points PP = Average number of test points

in the features of interest divided by total number of test points on the grid

VV = PP

7 test points out of 16 are in the particles. Volume fraction is 7/16 = 43.8%

Note: if the test point is on the edge of the features, we count as 0.5 point

Stereological Methods – Lines

IL=Average number of intersections between test lines and surfaces per unit test line length

SV = 2 IL

3 test lines (each 20 mm long) have18 intersections.

SV =2*18/(3*20)= 0.6/mm

Potential Problems (1)

2D sections can be deceitful - insufficient or inappropriate sampling

The sampling must be IUR (isotropic, uniform and random)

Potential Problems (2)

12 particle “profiles” 21 particle “profiles”

Biased Counting Method

Unbiased Counting Method

The Unbiased Counting Frame:

– A particle is counted if:

a) It lies completely inside the counting frame

Or

b) It crosses a green (inclusion) line but not a red (exclusion) line

Unbiased Counting Method

8 particles 8 particles

1

2

1

2

0

2

0

1

3

1

0

3

Automatic Measurement using ImageJ

Grayscale Image

Binary Image

Fill Holes

Clear Scale Bar

Cut Particles

Measurements

Live Demonstration

Launch ImageJ

Manual Estimation

Manual Estimation of Volume Fraction

Manual Estimation of Number Density

Summary

Stereology is a set of methods used to make estimates of geometrical features.

It provides methods for measuring volumes, surfaces and lines with stereological probes.

It only works when using appropriate sampling methods.