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References
Baddeley, A. 1., H. 1. G. Gundersen, L. M. Cruz-Orive (1986) "Estimation of surface area from vertical sections" Journal of Microscopy 142:259-276
Ballard, D. H., C. M. Brown (1982) "Computer Vision" Prentice Hall, Englewood Cliffs NJ
Barnes, F.L., S. G. Azavedo, H. E. Martz, et a!. (1990) "Geometric Effects in Tomographic Reconstruction" Lawrence Livermore National Lab. Rept. UCRL-ID-105130
Beddow, 1. K., G. C. Philip, A. F. Vetter (1977) "On Relating some Particle Profile Characteristics to the Profile Fourier Coefficients" Powder Tech . .l.8.: 19
Bevington, P. R. (1969) "Data Reduction and Error Analysis for the Physical Sciences" McGraw Hill, New York NY
Boyde, A. (1973) "Quantitative photogrammetric analysis and quantitative stereoscopic analysis of SEM images" 1. Microsc. 98:453
Buffon, G. L. L. (1777) "Essai d'arithmetique morale" Supp!. a I'Histoire Naturelle, Paris 1
Cahn, 1. W, 1. Nutting (1959) "Transmission quantitative metallography" Trans. AIME 215:526
Castleman, K. R. (1979) "Digital Image Processing" Prentice Hall, Englewood Cliffs NJ
Chandreshakar, S. (1943) "Stochastic problems in physics and astronomy" Rev. Mod. Phys. 15:86
Coster, M., 1.-L. Chermant (1985) "Precis D'Analyse D'lmages" Editions du Centre National de la Recherche Scientifique, Paris
Cruz-Orive, L.-M. (1976) "Particle size-shape distributions: the general spheroid problem" 1. Microscopy 107:235 and 112:153
Cruz-Orive, L.-M. (1983) "Distribution-free estimation of sphere size distributions from slabs showing overprojections and truncation, with a review of previous methods" 1. Microscopy 131 :265
Danielsson, P. E. (1980) Euclidean Distance Mapping" Compo Graph. 1m. Proc. 14:227-248
Davies, E. R. (1988) "On the noise suppression and image enhancement characteristics of the median, truncated median and mode filters" Patt. Recog. Lett. 7:87-97
DeHoff, R. T. (1962) "The determination of the size distribution of ellipsoidal particles from measurements made on random plane sections" Trans AIME 224:474
367
368 References
DeHoff, R. T. (1964) "The determination of the geometric properties of aggregates of constant size particles from counting measurements made on random plane sections" Trans AIME 230:617
DeHoff, R. T. (1977) "Geometrical meaning of the integral mean curvature" Microstructural Science, Volume 5, Elsevier-North Holland, New York, 331-345
DeHoff, R. T. (1978) "The stereo logical meaning of the area tangent count" Geometric Probability and Biological Structures: Buffon's 200th Anniversary, R. E. Miles and 1. Serra, editors, Springer Verlag, Berlin, 99-110
DeHoff, R. T. (1987) "Use of the disector to estimate the Euler characteristics of three dimensional microstructures" Acta Stereo!. 6: 133-140
DeHoff, R. T. (1993) "Thermodynamics in Materials Science" McGraw Hill, New York, NY, 365
DeHoff, R. T., F. N. Rhines (1968) "Quantitative Microscopy" McGraw Hill, New York NY
DeHoff, R. T., F. N. Rhines (1968a), ibid., 310- 316 Dougherty, E. R., 1. Astola (1994) "An Introduction to Nonlinear Image
Processing" SPIE, Bellingham WA Draper, N., H. Smith (1981) "Applied Regression Analysis, 2nd Edition" 1. Wiley &
Sons, New York Duda, R. 0., P. E. Hart (1972) "Use of the Hough transformation to detect lines
and curves in pictures" Comm. Assoc. Comput. Mach. 15: 11-15 Foley, 1. D., A. Van Dam (1984) "Fundamentals of Interactive Computer
Graphics" Addison Wesley, Reading MA Frank, 1. (1992) "Electron Tomography" Plenum Press, New York NY Frisby, 1. P. (1980) "Vision: Illusion, Brain and Mind" Oxford Univ. Press, Oxford
UK Gibbons, 1. D. (1985) "Nonparametric Methods for Quantitative Analysis, 2nd
Edition" American Sciences Press, Columbus, OH Gokhale, A. M. (1992) "Estimation of length density Lv from vertical slices of
unknown thickness" 1. Microscopy 167:1- 8 Gonzalez, R. c., P. Wintz (1987) "Digital Image Processing, 2nd Edition"
Academic Press, New York NY Gordon, R. (1974) "A tutorial on ART" IEEE Trans. NS-21:78- 93 Gundersen, H. 1. 0. (1986) "Stereo logy of arbitrary particles" 1. Microsc. 143:
3-45 Gundersen, H. 1. G., P. Bagger, T. F. Bendtsen, S. M. Evans, L. Korbo, N.
Marcussen, A. Moller, K. Nielsen, 1. R . Nyengaard, B. Pakkenberg, F. B. Sorensen, A. Vesterby, M. 1. West (1988) "The new stereo logical tools: Disector, fractionator, nucleator and point sampled intercepts and their use in pathological research and diagnosis" Acta Path. Microbio!. Immuno. Scan. 96:857- 881
Gundersen, H. 1. G., T. F. Bendtsen, L. Korbo, N. Marcussen, A. Moller, K. Nielsen, 1. R. Nyengaard, B. Pakkenberg, F. B. Sorensen, A. Vesterby, M. 1. West (1988) "Some new, simple and efficient stereo logical methods and their use
References 369
in pathological research and diagnosis" Acta Path. Microbiol. Immuno. Scan. 96:379-394
Gundersen, H. 1. G., E. B. Jensen, R. Osterby (1978) "Distribution of membrane thickness determined by lineal analysis" 1. Microscopy 113:27
Gundersen, H. 1. G., E. B. Jensen (1987) "The efficiency of systematic sampling in stereology and its prediction" 1. Microsc. 147:229-263
Gundersen, H. 1. G., R. Osterby (1981) "Optimizing sampling efficiency in stereological studies in biology, or 'Do More Less Well!'" 1. Microscopy 121:65-73
Halford, K. 1., K. Preston (1984) "3-D Skeletonization of elongated solids" Compo Vis. Graph. 1m. Proc. 27:78-91
Ham, Y. S. (1993) "Differential Absorption Cone-Beam Microtomography" Ph. D. Thesis, North Carolina State University
Herman, G. T. (1980) "Image Reconstruction from Projections-the Fundamentals of Computerized Tomography" Academic Press, New York NY
Heyn, E. (1903) "Short reports from the Metallurgical and Metallographic Laboratory of the Royal Mechanical and Testing Institute of Charlottenburg" Metallographist 6:37
Holmes, A. (1927) "Petrographic methods and calculations" Murby, London Hough, P. V. C. (1962) "Method and Means for Recognizing Complex Patterns" U.
S. Patent 3069654 Howard, C. v., M. G. Reed (1988) "Unbiased Stereology, Three Dimensional
Measurements in Stereology" BIOS Scientific Publishers, Oxford, UK Howard, C. v., M. G. Reed (1988a) ibid., 39-54 Howard, C. v., M. G. Reed (1988a) ibid., 89-95 Hull, F. c., W 1. Houk (1953) "Statistical Grain Structure Studies, Plane Curves of
Regular Polyhedrons" Trans AIME 197:565 Inoue, S. (1986) "Video Microscopy" Plenum Press, New York NY Jain, A. K. (1989) "Fundamentals of Digital Image Processing" Prentice Hall,
London UK Jeffries, Z., A. H. Kline, E. B. Zimmer (1916) "Determination of grain size in
metals" Trans. AIME 57:596 Johnson, E. M., 1. 1. Capowski (1985) "Principles of reconstruction and three
dimensional display of serial sections using a computer" pp. 249-263 in The Microcomputer in Cell and Neurobiology Research (R. Mize, ed.), Elsevier, New York NY
Kak, A. c., M. Slaney (1988) "Principles of Computerized Tomographic Imaging" IEEE Publ. PC-02071
Kendall, M. G., P. A. Moran (1963) "Geometrical Probability" No. 10 in Griffith's Statistical Monographs, Charles Griffith, London UK
Kriete, A. (1992) "Visualization in Biomedical Microscopies: 3D Imaging and Computer Applications" VCH Publishers, Weinheim Germany
Kurzydlowski, K. 1., B. Ralph (1995) "The Quantitative Description of the Microstructure of Materials" CRC Press, Boca Raton FL
Lobregt, S., P. W Verbeek, F. C. A. Groen (1980) "Three-dimensional ske1etonization: principle and algorithm" IEEE Trans PAMI-2:75-77
370 References
Lord, G W, T. F. Willis (1951) "Calculations of air bubble size distribution from results of a Rosiwal traverse of aerated concrete" ASTM Bulletin 177:56
Marr, D., T. Poggio (1976) "Cooperative computation of stereo disparity" Science 194:283-287
Matheron, G (1975) "Random Sets and Integral Geometry" 1. Wiley & Sons, New York NY
Mayhew, T. M., H. 1. G Gendersen (1996) "If you assume, you can make an ass out of u and me: a decade of the disector for stereological counting of particles in 3D space" 1. Anat. 188: 1-15
Medioni, G, R. Nevatia (1985) "Segment-based stereo matching" Compo Vis. Graph. 1m. Proc. 31:2-18
Miles, R. E. (1976) "Estimating aggregate and overall characteristics from thick sections by transmission microscopy" 1. Microscopy 107:227
Nauman, E. B., T. 1. Cavanaugh (1998) "Method of calculating true particle size distributions from observed sizes in a thin section" Microscopy and Microanalysis 4:122-127
Neal, B., 1. C. Russ, 1. C. Russ (1998) "A superresolution approach to perimeter measurement" 1. Compo Assisted Microscopy 10(1):11-21
Ohser, 1., M. Nippe (1997) "Stereology of cubic particles: various estimators for the size distribution" 1. Microscopy 187:22-30
Pavlidis, T. (1980) "A thinning algorithm for discrete binary images" Compo Graph. 1m. Proc. 13:142-157
Peleg, S., 1. Naor, et al. (1984) "Multiple Resolution Texture Analysis and Classification" IEEE Trans PAMI-6:518
Pratt, W K. (1991) "Digital Image Processing, 2nd edition" 1. Wiley & Sons, New York NY
Roberts, N., M. Reed, G Nesbitt (1997) "Estimation of the connectivity of a synthetic porous medium" 1. Microsc. 187(2):110--118
Rosenfeld, A., A. C. Kak (1982) "Digital Picture Processing, 2nd Edition" Academic Press, New York NY
Russ,1. C. (1993) "Method and application for ANDing features in binary images" J Compo Ass. Microsc. 5(4):265-272
Russ, 1. C. (1994a) "The Image Processing Handbook, 2nd Edition" CRC Press, Boca Raton FL
Russ,1. C. (1994b) "Fractal Surfaces" Plenum Press, New York NY Russ, 1. C. (1995a) "Computer-Assisted Manual Stereology" J Compo Ass. Microsc.
1(1), 35--46 Russ,1. C. (1995b) "Thresholding Images" J Compo Ass. Microsc.1(3), 141-164 Russ, 1. c., 1. C. Russ (1989) "Topological measurements on skeletonized three
dimensional networks" 1. Compo Assist. Microsc. 1: 131-150 Saltykov, S. A. (1958) "Stereometric Metallography, 2nd edition" Metallurgizdat,
Moscow, USSR Saltykov, S. A. (1967) "The determination of size distribution of particles in an
opaque material from the measurement of the size distribution of their sections" Stereology, Springer Verlag, New York, p. 163
References 371
Santalo, L. A. (1976) "Integral Geometry and Geometric Probability" Addison Wesley, Reading MA
Schwarz, H., H. E. Exner (1983) "The characterization of the arrangement of feature centroids in planes and volumes" J. Microsc. 129: 155
Serra, J. (1982) "Image Analysis and Mathematical Morphology" Academic Press, London UK
Sterio, D. C. (1984) "The unbiased estimation of number and sizes of arbitrary particles using the disector" J. Microsc. 134: 127-136
Thaulow, N., E. W White (1971) "General method for dispersing and disaggregating particulate samples for quantitative SEM and optical microscope studies" Powder Techn. 5:377
Underwood, E. E. (1970) "Quantitative Stereology" Addison Wesley, Reading MA Underwood, E. E. (1970a) ibid., 38-43 Underwood, E. E. (1970a) ibid., 48-73 Wasen, J., R. Warren (1990) "A Catalogue of Stereological Characteristics of
Selected Solid Bodies, Volume 1: Polyhedrons" Dept. of Engineering Metals, Chalmers Univ. of Technology, Goteborg, Sweden
Weibel, E. R. (1979) "Stereological Methods" Academic Press, London U.K. Weibel, E. R., D. M. Gomez (1962) "A principle for counting tissue structures on
random sections" J. Appl. Physiol. 17:343 Wicksell, S. D. (1925) "The Corpuscle Problem" Biometrica 17:84; 18:152 Zhao, H. Q., I. F. MacDonald (1993) "An unbiased and efficient procedure for a
3703-D connectivity measurement as applied to porous media" J. Microsc. 172:157-162
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