Post on 11-Jan-2016
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.