References - Springer978-1-4615-1233-2/1.pdf · References 369 in pathological ... Howard, C. v., M. G. Reed (1988) "Unbiased Stereology, Three Dimensional Measurements in Stereology…

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Index

Accuracy, 149-150 Acoustic microscopy, 348 Adobe Photoshop, 191 Aerial mapping, 351 Algebraic methods, 348 Alignment, 330, 346 Analysis-of-variance (ANOVA) test, 168

critical values, 168 Anisotropy, 2, 28, 60, 65, 90, 313

degree of, 315-316, 319

grain structure of rolled steel, 316 identification of, 326 muscle fiber structure, 317

Area fraction measurement of, 45-46, 48

three-phase structure, 47 Area fraction, 2, 5, 8, 16, 231 Area point count, 42, 69-70 Area tangent count, 79, 102, 108 Area, 36

Aspect ratio, 308 Associations, 42 Asymptotic limit, 167 Automatic algorithms, 235 Axial ratio, 307, 310

Bertrand's paradox, 287-290 illustration for, 292

Bias, 8, 85, 103, 127, 152, 253, 271, 278, 280, 337

directional, 320 estimation, 114 potential, 85

Bimodal distribution, 161 Binary image, 224-227, 235, 237, 268, 333 Binomial theorem, 169 Blobs, 231 Boolean logic, 265, 268 Boundary orientation, 320-322

measurement of, 322 Branching structure, 341 Brightness, 196-197, 254, 261

correction for nonuniform, 194-198 Brightness gradient, 320

Brightness thresholding, 8 Buffon needle problem, 290-293, 296, 318-

319 geometry for, 292

Caliper diameter, 88-89 mean, 88-90, 108

estimation of, 90, 94 Camphor-napthalene eutectic wax, 332 Capillary effects, 90, 93 Carburization, 323 Cartesian coordinate system, 112-125

application of line probes, 115-118 application of point probes, 112, 115-118 disectors in three-dimensional space, 118-119 planes in three-dimensional space, 118

Cavalieri's principle, 17, 54, 124 Central limit theorem, 156 Centroid, 248 Chemical deposition, 3 Chemical etching, 3, 227 Circular image, 100-101 Closed surface, 92 Clusters, 324, 335

examples of, 325 Colatitude, 116 Color absorption, 353 Color coding, 321, 329 Color sensitivity, 184 Compression methods, 188 Computed tomographic methods, 347 Computer-based image analysis, 320; see also

Image Concave surface, 80-81 Confidence interval, 121

Confidence limit, 175 Confocal light microscopy, 331 Confocal microscopy, 82, 346-347 Connectivity, 5, 37-38, 79, 81-82, 108, 145, 237

estimation of, 84 multiply, WI

Contrast

373

manipulation, 193-194 reversal, 194, 196

374

Convex shapes, 80-81, 303, 308 Correlation coefficient, 177-179 Counting experiment, 15 [ Counting frame, 22 Cross correlation technique, 35[ Cumulative distribution, [72-173 Curvature, [3-[4, 79, 93, [45-[46

concept of, [3 Gaussian, 93 measurement of, [4 surface elements, [45-146 surface, 90-92

Cycloid curve, 67-76 Cycloids, 65, 139-[41,208,342-343

Deconvolution, 346 Deformation, 41

directional, 41 Degrees of freedom, 167 Delineation, 315, 347 Density variation, 3 Depth of field, 346 Depth resolution, 347 Differentia[ geometry, 91-92 Digital cameras, 186-187 Dihedral angle, 104-107, 109 Directional bias, 320 Director vector, 140 Disector probes, 6, 16, 20-21, 27-28, 82, 84,

108, 118-119, 142-144 application of, 145 diagram of, 143-144 implementation of, 142 uses of, 142

Disector volume element probe, 20 Dislocation pinning, 12 Distance map, 329 Distortion, 200-202, 345 Dye sublimation, 189-190

Edge, 31, 95, 104-106, 109,255 orientation, 257, 259

Edge detector, 255 Edge orientation, 232

measurement of, 321 Edge running, 202 Edge sharpness, 203 Edge-enhancement operator, 267 Electron diffraction, 348 Electron microscopy, 331 Electron tomography, 348 Ellipsoids, 303

unfolding size distribution, 306-308

Encoding algorithms, 188 End cap problem, 339-340 Erosion algorithm, 245 Euclidean Distance Map, 246, 269, 327

illustration of, 328

Index

Euler characteristic, 37, 82, 84, 86, 88, 94, 101-103, 108

Event, 6-7, 20 Exclusion edge, 144 Expected value, 9, 16,23-24, 27, 46, 50, 114,

341 Expected value theorems, 8, 23, 27, 111

Face-centered cubic lattice, 359 Feature count, 22 Features

alignment of, 330 geometrical properties of, 4-6 set, 20

Filtered back projection, 348 Filters, 197-200

Gaussian, 198 Lap[acian, 202-203 median, 199

Flower plot, 175-176 Fluorescence imaging, 346-347 Fourier transformation, 358 Fractal compression, 189 Fractal dimension, 247, 261 Fractionator, 120, 124-125 Frame grabbers, 184 Frequency distribution, 152 Frequency space, 198, 202

Gamma rays, 349 Gaussian curvature, 13, 93 Gaussian distribution, 156-157, 159

equation, 156-157 Gaussian filter, 198, 265 Gaussian noise, 233 Genus, 145 Geometric modeling

Bertrand's paradox, 287-290, 292 bias in, 271, 278, 280; see also Bias Buffon needle problem, 290-293, 296 effects of rotation, 282 intercept lengths in

cube, 278, 294 sphere, 274-277, 293 square, 278, 281, 294 three-dimensional images, 280-286

intersection of planes with objects, 286-289 methods of, 272-274

Index

Geometric modeling (cont.)

methods of (cont.)

analytic vs. sampling, 272-273 Monte Carlo, 273, 277

overview of, 271-272 random line generation, 279 spherical coordinate system in, 281

Geometric probability, 271 Geometric properties, 19,24,27-29 Global parameters, 361 Global properties, 29, 36

ratios of, 39 Golgi-stained neurons, 364-365 Goodness of fit, 177-178 Gradients, 39, 114, 255, 320, 323

concentration, 323 detection of, 329 examples of, 324 irregular, 327

Grain boundary, 252, 254, 313, 315 Grain orientation, 322 Grain size, 10, 210

calculation of, 211 determination of, 252 number, 13

Grain structure, 12, 254, 340 Grey scale variation, 231, 261 Grid overlay, 12, 204-209, 254

computer measurement of images by, 223-229 routines for generation of, 211-221 sampling method, 129-131 sizing of, 16-17 superposition, 20-22

Hardness indentation, 142, 346 Harmonic analysis, 247 High field gradient, 349 Histogram, 152-153 Hough space, 268 Hough transform, 330

illustration of, 329 Hubble telescope, 202 Hue-Saturation-Intensity (HSI) representation,

193

Image; see also Microstructure, Three­dimensional imaging, Three­dimensional structure, Two­dimensional structure

analysis systems, 1, 19, 270, 320 application in medical diagnosis, 347-349 archiving, 188 area fraction estimation, 231

375

Image (cont.)

area measurement, 237 bias in stereological measurements, 337-340 binary, 224-227, 235, 237, 268, 333 brightness, 254 carbon steel, 3 circular, 100-101 common defects, 192 computer measurement of, 223

data acquisition, 255-261 multiple combination, 261-268 pixels for area measurement, 229-237 position, 246-248 shape, 246-248 size, 237-246 structural dimensions, 226 thresholding, 249-255 using grids, 223-229

computer-assisted methods in generation of, 183-211, 320

typical equipment setup, 183-184 contrast manipulation, 193-194 correcting nonuniform brightness, 194-198 correction of, 249, 332 dark etched iron carbide, 261 display, 187-191 effect of finite section thickness on, 331-344 effect of shape variation on, 297, 303 effects of noise, 232-233 effects of opaque phase on, 338 end cap correction, 340 enhancement, 202-203 error sources in measurement, 231 etched aluminum, 254-255 feature measurements, 237-248 filtering, 197-200 finite sizing of, 249 fluorescence, 249, 269, 346-347 human brain, 352 graphite nodules in cast iron, 305 grey scale processing, 261 grid overlays, 12, 204-209, 254 immunofluorescence, 346 integrated circuit, 257 ion microscopic, 359 latex spheres, 335 layer thickness measurement, 228, 248 light micrographs

curds, 260 etched steel, 261-262 whey, 260

light microscope, 3 linear intercepts in spheres, 298

376

Image (cont.) magnetic resonance, 349, 353-354 measurements within sections, 340-344 metal coating, 227, 229, 239-244 nerve axons, 343 noise reduction, 198-200 particle-substrate interaction on, 331 plane intersections on, 300

effect of non-spherical shape, 303 effect of spherical shape, 301-305

processing operations, 191-193, 268-270 steps in, 191-192

projected, 2, 331-339, 342-343 illustration of particles in thick section,

334-336 linear structures, 340-342 plant root structures, 341, 344

rat liver, 3 rectifying distortion, 200-202 red blood cells, 249-250 reference, 195 resolution, 184-187 rock pile, 266 role of particle distribution on, 331-332 rolled metals, 208 rotation effects on, 232-239 sampling of, 204

basic stereological calculations, 210-211 grid overlays, 204-209

seismic, 348 spherical, 79-82, 101, 108, 116, 145 statistical interpretation of data, 149-181 stereo, 351 storage, 187-191 surface roughness, 247 three-dimensional; see Three-dimensional

imaging three-phase alloy, 235 transmission electron microscope, 3, 346 two-phase ceramic, 251, 253 underwater, 348 unfolding size distribution, 297-312 volume fraction estimation, 226, 261

Image reconstruction, 347 medical diagnosis, 348

Immunofluorescence cell image, 346 Inbiased estimation, 23, 27-28 Inclusions, 42 Integral mean curvature, 24, 90-99, 102-103,

105-109 concept of, 79 cylinder, 92 sphere, 93

Intercept area distribution sphere vs. cube, 290

Index

Intercept length, 10, 13, 230, 283, 286, 298, 311, 313, 316

distribution with intersecting spheres, 298 Intersection point, 7 Inverse methods, 347 Inverse reconstruction

principle of, 347 Ion microscopic image

two-phase Fe-Cr alloy, 359 Isometric display, 279-280 Isotropic line probes, 136-142; see also Line

probes Isotropic planes, 132 Isotropy, 41, 341, 358 Isotropic-Uniform-Random (lUR) sampling, 8,

28 applications of, 313 conditions of, 345 procedures of, 127 -148

application to structural networks, 145-148

disector method, 142-144 grid method, 129-131 isotropic line probes, 136-142 isotropic planes, 132-136 sampling planes, 131-132

JPEG method, 189

Kolmogorov-Smimov test, 171, 173 application of, 173-174 critical values, 174

Kruskal-Wallis test, 170 critical values, 172 principle of, 171

Kurtosis, 160-161, 163

Lamellar structure, 103, 310 Laplacian filter, 202-203 Length, 37 Length fraction, 5 Light microscopy, 331, 346 Line intercept count, 22-23, 42, 56-57, 63, 65 Line probes, 6, 10, 20-21, 26-28, 133, 297,

310 Lineal features, 69-71, 74 Linear intercept, 274, 299-300, 302

arbitrary non-convex shape, 285 cube, 282 cylinder, 285 polyhedron, 284

Index

Linear intercept (cont.) tetrahedron, 284 torus, 285 unfolding, 309

Linear regression, 175-179 computer procedure for, 177

Linear structures, 340, 342 Local surface normal, 41, 79 Log-normal distribution, 165-166 Look-up plane, 85, 88, 108

Magnetic resonance imaging, 349 heart muscle, 353-354

Mann-Whitney test, 169, 17l critical values, 170

Matched points, 351 Mean, 155-157, 159-160, 162 Mean free distance, 12 Mean intercept length, 128 Mean lineal intercept, 39 Mean particle diameter, 6 Mean value, 23, 114, 310 Median, 155-156 Median filter, 199 Metallographic microscopy, 331 Method of vertical sections, 66, 118, 124 Metric properties, 4-5, 35, 37, 44 Microscopy

acoustic, 348 confocal, 82, 346-347 confocal light, 331 electron, 348 ion, 359 light, 3, 260-262, 331, 346 metallographic, 331 reflected light, 346-347 scanning electron, 331, 350-351 transmission electron, 3, 335, 343

Microstructure, 19, 21 anisotropy in, 41-42 associations in, 42-43 characterization of, 29, 33

qualitative state, 29, 31-35 quantitative state, 29, 35-39 topographic state, 29, 39-40

concept of phase in, 29 description of, 29 effects of gradients on, 39-41 effects of inclusions in, 42 feature sets in, 20, 29, 33-35

connectivity in, 37 geometric properties, 38 global properties, 29

Microstructure (cont.)

feature sets in (cont.)

isotropy in, 41 spatial distribution, 40-42

geometric properties of, 29, 44 classes of, 44

global metric parameters of, 345 global properties, 36

estimation of, 40 ratios of, 39

image reconstruction of, 347 metric properties of, 35 nonuniformities, 39 overview of, 29 particle distribution in, 32 phase distribution in, 31-36 topological properties, 37

measurement of, 38 Microtoming, 326 Minkowski's formula , 94, 105 Mode, 155-156 Monte-Carlo method, 273, 277

intercept length frequency polyhedra vs. sphere, 286

Morphological operators, 224, 268 Multiple regression, 178

stepwise, 179 Multiply connectivity, 101 Muralia, 14, 95, 97-98

377

Nearest neighbor distance, 12, 248, 324-326 Neighbor logic, 231 Neighborhood operator, 224 Neutrons, 349 NIH Image Program, 205 Noise, 198-200, 232 Nonlinear regression, 179-181 Nonparametric tests, 168-175 Nonuniformities, 39, 313, 323 Normal distribution, 158 Normal plane, 91, 118 Normality, 160-161, 175 Nucleator, 16 Number, S Number density, 23 Number-weighted mean volume, IS

Opaque phase, 338-339 Optical sectioning, 142, 346-347 Orientation, 133, 135

boundary, 320-322 edge, 257, 259 preferred, 313, 316

378

Orientation (cant.)

preferred (cant.)

degree of, 319-321 examples of, 318 illustration of, 327

random, 134, 283, 331-332 sensitivity, 232

Orientator, 136 implementation of, 137

Osculating circle, 90 Outcome, 20 Overprojection, 338-339

Parabolic points, 93 Parallax, 202, 349-352 Parametric tests, 165-168, 175 Particle

counting, 310 diameter, 6 distribution, 15 height, 6 size, 90 volume, 6

Perimeter measurement of, 56-63

Phase, 210 Photomicrograph, 23 Pixel counting, 229, 232 Plane intersection, 300 Plane probes, 6, 20-21, 24, 27-28, 98, 133,

297, 341 Planimeter, 55 Platonic solid, 134 Point count, 36, 45-56, 124, 128 Point fraction, 5, 10, 16, 22-23, 48, 112 Point plot, 175-176 Point probes, 20, 27-28, 111-1I4, 127 Points, 31, 145 Point-sampled intercept length method, 14- 15 Poisson distribution, 163-164

equation, 163 Poisson random process, 324 Polishing relief, 338 Polyhedra

examples of, 9 regular, 134

Polymer composites, 316 Population mean, 24 Pores, 300 Porosity, 35 Potential bias, 85 Precision, 149-150 Principal components analysis method, 179

Principle direction, 91 Principle normal curvature, 91-92 Printers, 189 Probability, 154, 160, 175

estimation of, 154 Probe-event combination, 21-24

Index

Probes, 20; see also Plane probes, Line probes, Disector probes

construction of, 20 plane, 6, 98, 20-21, 24, 27-28, 133, 297,

341 stereological application of, 20-24 types of, 20

Projected area, 25

Quadruple points, 33

Random distribution, 324 Random line generation, 279 Random noise, 232 Random number generator, 273 Random orientation, 134, 283, 331-332 Random points generation, 129 Random sampling, 127 Random systematic sample, 120-121 , 125 Randomness, 127, 273 Rank correlation, lSI Rank operator, 196-198 Ray tracing, 353 Reconstruction methods, 349 Reference plane, 85, 88, 108 Reflected light microscopy, 346-347 Regularity, 127 RND function, 273, 275 Rolled metals, 313, 316 Rose plot, 60-61, 314, 326

aspect ratio of, 321

Saddle surface, 13, 80-81, 145-147 Sample mean, 24, 27 Sampling bias, 127 Sampling design, 22-23, 28

application of line probes, 115-118, 125 application of point probes, 111-1I4, 125 Cartesian coordinate system, 112-125 disectors in three-dimensional space, I1S-

119, 125 overview of, III planes in three-dimensional space, 118, 125 strategies in stereology, 119-124

Sampling grid, I3l Sampling planes, 131-132 Scanning electron microscopy, 331

Index

Scanning electron microscopy (cont.)

image of yeast cells, 350 mapping, 351

Scatter plot, 175 Seismic imaging, 348 Self-avoidance, 12, 129,248, 324 Sequential polishing method, 346 Serial methods, 345 Serial sectioning, 79, 82, 345, 355

cochlea, 355-356 Shape 35, 247

coefficients, 310 descriptor, 247 factors, 307, 310

Sharpening, 202 Sharpness, 203 Sine weighting, 67, 74 Size distribution

unfolding, 297-312 Skeletons, 245 , 247 Skewness, 160-162 Smooth boundary, 235-236 Smooth surface, 91 Sobel operator, 252, 256, 320, 361 Solarization, 194, 196 Sound waves, 348 Space curve, 104 Spatial averaging, 198 Spearman correlation, 180 Specific curvature, 5 Specific line length

definition of, 5 Specific surface area

definition of, 5 estimation of, 319 mean, 6

Sphere alpha matrices, 304 distribution of planar intercepts, 302 sectioning, 301-302 unfolding method, 303

Spherical coordinate system, 65, 281 Spherical harmonics, 365 Spherical image, 79-80, 101, 108, 116, 145

concept of, 79 net, 81 per unit volume, 82

Spherical neighborhood, 358, 360 Standard deviation, 157, 159-160, 162 Standard error of the mean, 159 Statistical analysis

analysis-of-variance (ANOVA), 168 binomial theorem, 169

Statistical analysis (cont.)

calculation of parameters in, 159 central limit theorem, 156 cumulative distribution, 172-173 data comparison, 154 degrees of freedom, 167 distribution of values, 152-155 Gaussian distribution, 156-157 Kolmogorov-Smirnov test, 171, 173 Kruskal-Wallis test, 170 kurtosis, 160-163 linear regression, 175-179 log-normal distribution, 165-166 Mann-Whitney test, 169, 171 mean, 155-157, 159-160, 162 median, 155-156 mode, 155-156 multiple regression, 178-179 nonlinear regression, 179-181 non parametric tests, 168-175 normal distribution, 158 normality , 160-161, 175 parametric tests, 165-168, 175 Poisson distribution, 163-164 skewness, 160-162

379

sources of variability in measurement, 149-152

Spearman correlation, 180-181 standard deviation, 157, 159-160, 162 standard error of the mean, 159 Student's t-test, 165- 167 variance, 157, 159-160 Wilcoxon test, 168, 170-171

Steradian, 80 Stereo image, 351 Stereology

application to single objects, 16-18 basic rule of, 229 bias, 8; see also Bias classical rules in, 8 definition of, I, 18, 271, 349 expected value relationships in, 24 fundamental relationships in, 8-10, 23-27 grid superposition in, 20-22 ground rules for application of, 27-28 IUR sampling in, 8 measurement procedures in, 22-23, 45-77,

79-109 objects with curvature, 79

anisotropy, 90 area tangent counts, 79 bias, 85, 103 caliper diameter, 88-90, 94, 108

380

Stereology (cont.) measurement procedures in (cont.)

objects with curvature (cont.) capillary effects, 90, 93 classes of surface elements, 92 connectivity, 79, 81-82, 108 dihedral angle, 104-107, 109 disector analysis, 82, 84, 108 effects of edges, 104-108 Euler characteristic, 82, 84, 86, 88, 94,

101-103, 108 look-up plane, 85, 88, 108 mean curvature, 90-99, 102-103, 105-

109 multiply connectivity, 101 muralia, 95, 97-98 reference plane, 85, 88, 108 spherical image, 79-80 sweeping line probes, 99-104 sweeping plane probe, 83, 88-89, 98 tangent planes, 79, 82-86 topological properties, 79 tubules, 97, 99 volume tangent count, 79, 101

three-dimensional features, 79-90, 104-108

mechanics of, 20-24 microstructure of two-phase metal, II overview of, 4, 19-20, 24, 28 probe-event combinations in, 21-24 probes in, 4, 6-7, 21-28; see also Plane

probes, Line probes, Disector probes relationships, I sample design, 23 second-order, 14-16 three-dimensional structures, 24-27, 51-56,

63-76 two-dimensional structures, 45-51, 56-63 typical experiment of, 24 typical procedures in, 6-8 unbiased estimation in, 23, 27-28 uses of, 1, 19

Stereoscopy as three-dimensional technique, 349-351 image of volumes, 351 principle of measurement, 350

Structured random sample, 55 method, 127, 129-131, 137

Student's I-test, 165-167 critical values, 167

Surface area density, 23, 36, 64, 68 measurement of, 63

Surface area/unit volume, 283 estimation of, 210, 227

Surface curvature, 90-92 concept of, 90 mean, 90-99 right circular cylinder, 92

Surface elements, 31 classes of, 92

Surface energy, 105 Surface modeling, 351 Surface pits, 332 Surface rendering, 354-355 Surface roughness , 247, 261 Surface-to-volume ratio, 10 Sweeping line probe, 99-104

concept of, 101 Sweeping plane probe, 83, 88-89 Sweeping tangent plane, 82-83, 86 Symmetric distribution, 155 Symmetry, 275 Synchrotron, 348 Systematic random sample, 49

Tangent count, 103, 108 Tangent diameter, 25 Tangent plane, 79, 82-86 Tessellation, 29, 200

Index

idealized illustration of space filling, 30 single phase, 29

Texture operator, 259, 261 Three-dimensional imaging

global parameters in, 361 limitations of stereology in, 345 measurement of, 361-365 processing of, 358-361 reconstruction methods in, 358

Golgi-stained neurons, 364 role of inversion in, 347 serial methods for data acquisition, 345 visualization of, 352-358

Three-dimensional structure, 19-20,22-27, 51-56, 63-76

basic elements of, 1-2 geometric properties of, 4 measurement of, 6 metric properties of, 4 stereological measurement of line length, 69-76 surface area, 63-69 volume fraction, 51-56

Thresholding, 231-235, 249-255, 261 Tomographic methods, 347, 349

reconstruction, 348

Index

Topological properties, 5, 37-39, 44, 79, 145 estimation of, 345 measurement of, 38

Toroids, 332 illustration of projected image, 333

Torus, 147 Transfer function, 193 Transmission electron microscope

image of latex spheres, 335 image of nerve axons, 343

Transmission imaging, 346 Transparent specimen, 74 Triple lines, 2, 104 Tubular structures, 69, 97, 99 Two-dimensional structure, I, 45-51, 56-63

stereological measurements of area fraction, 45-56 perimeter, 56-63

Two-way histogram, 175-176

Unbiased counting frame, 85 Underwater image, 348 Unfolding method, 340

size distribution, 297-312 Unit sphere, 116, 145 Unsharp mask, 202-203

Variance, 157, 159-160 Vergence, 351 Vertical sectioning method, 66, 118, 124, 135,

138-139, 210

Video cameras, 183, 198 Video digitizers, 184 Voids, 332

381

Volume fraction, 8, 10, 23-24, 35-36, 112, 114, 128-131, 283

definition of, 5 estimation of, 128, 210, 226 measurement of, 51-52 relation, 112, 114

Volume probes, 6, 142-144 Volume tangent count, 79, 101 Volumetric display, 353-355, 364 Volume-weighted mean volume, 14 Voronoi tessellation, 200 Voxel array, 351-353, 359, 361 Voxels, 17, 347

Watershed segmentation, 249, 253 Weighted averaging, 198 Weighted regression, 177 Wilcoxon test, 168, 170-171

critical values, 170 principle of, 169

X-ray CAT scan, 347-348 X-ray maps, 261, 264 X-ray microtomography, 361-362

Zero curvature, 13 Zero-dimensional feature , 2