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

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) Biased Counting Method 12 particle “profiles”

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 1 2 1 1 3 1 2 3 2 8 particles 8 particles

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.