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Tables of Contents for Practical Stereology
Chapter/Section Title
Page #
Page Count
Introduction
1
18
Elements of microstructure
1
3
Geometric properties of features
4
2
Typical stereological procedures
6
2
Fundamental relationships
8
2
Intercept length and grain size
10
3
Curvature
13
1
Second order stereology
14
2
Stereology of single objects
16
3
Basic Stereological Procedures
19
10
What stereology is
19
1
How stereology works
20
4
Why stereology works
24
3
Ground rules for applying stereology
27
2
Geometry of Microstructures
29
16
The qualitative microstructural state
31
4
The quantitative microstructural state
35
4
Metric properties
35
2
Topological properties
37
2
Ratios of global properties
39
1
The topographic microstructural state
39
6
Gradients: variation with position
39
2
Anisoptropies: variation with orientation
41
1
Associations
42
3
Classical Stereological Measures
45
34
Two-dimensional structures; area fraction from the point count
45
6
Volume fraction from the point count
51
5
Two-dimensional structures; feature perimeter from the line intercept count
56
7
Three-dimensional structures: surface are and the line intercept count
63
6
Three-dimensional microstructures; line length and the area point count
69
10
Less Common Stereological Measures
79
32
Three-dimensional features: topological properties and the volume tangent count
79
9
Three-dimensional features: the mean caliper diameter
88
2
Mean surface curvature and its integral
90
9
The sweeping line probe in two dimensions
99
5
Edges in three-dimensional Microstructures
104
7
Sample Design in Stereology
111
16
Population of point probes
111
4
Population of lines in two dimensions
115
1
Line probes in three dimensions
115
3
Planes in three-dimensional space
118
1
Disectors in three-dimensional space
118
1
Sampling strategies in 3D
119
8
Procedures for IUR Sampling
127
22
Volume fraction
128
3
Sampling planes
131
1
Isotropic planes
132
4
Isotropic line probes
136
6
Volume probes--the Disector
142
3
Networks
145
4
Statistical Interpretation of Data
149
34
Sources of variability in measurement
149
3
Distributions of values
152
3
The mean, median and mode
155
1
The central limit theorem and the Gaussian distribution
156
1
Variance and standard deviation
157
3
Testing distributions for normality--skew and kurtosis
160
1
Some other common distributions
161
4
Comparing sets of measurements--the T-test
165
3
Nonparametric comparisons
168
7
Linear regression
175
4
Nonlinear regression
179
4
Computer-Assisted Methods
183
40
Getting the image to the computer
183
4
Display and storage
187
4
Image processing
191
13
Contrast manipulation
193
1
Correcting nonuniform brightness
194
4
Reducing image noise
198
2
Rectifying image distortion
200
2
Enhancement
202
2
Overlaying grids onto images
204
6
Basic stereological calculations
210
1
Appendix
211
12
Computer Measurement of Images
223
48
Measurement using grids
223
6
Measurement area with pixels
229
8
Measurement parameters--size
237
9
Other feature measurements: shape and position
246
3
Image processing to enable thresholding and measurement
249
6
Image processing to extract measurable information
255
6
Combining multiple images
261
10
Geometric Modeling
271
26
Methods: analytic and sampling
272
3
Sphere intercepts
275
1
Intercept lengths in other bodies
275
5
Intercept lengths in three dimensions
280
6
Intersections of planes with objects
286
1
Bertrand's paradox
287
3
The Buffon needle problem
290
3
Appendix
293
4
Unfolding Size Distributions
297
16
Linear intercepts in spheres
298
2
Plane intersections
300
3
Other shapes
303
6
Simpler methods
309
1
Lamellae
310
3
Anisotropy and Gradients
313
18
Grain structures in rolled metals
313
7
Boundary orientation
320
3
Gradients and neighbor relationships
323
4
Distances and irregular gradients
327
3
Alignment
330
1
Finite Section Thickness
331
14
Projected images
331
6
Bias in stereological measurements
337
3
Measurements within sections
340
5
Three-Dimensional Imaging
345
22
Limitations of stereology
345
1
Serial methods for acquiring 3D image data
345
2
Inversion to obtain 3D data
347
2
Stereoscopy as a 3D technique
349
3
Visualization
352
6
Processing
358
3
Measurement
361
6
References
367
6
Index
373