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| Ïîèñê ïî óêàçàòåëÿì |
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| Serra J. — Image Analysis and Mathematical Morphology |
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| Ïðåäìåòíûé óêàçàòåëü |
Linear size distribution, digital 37
Linear size distribution, digitalization 360
Local approach 232 440
Local approach for the covariance 275
Local knowledge and mask corrections 49
Local knowledge for erosion 46 61
Local knowledge for parameters 128
Local knowledge, example 406
Local knowledge, principle of 11 62 239
Local knowledge, sequential operations 396
Local knowledge, size distributions 334 357—358
Logistic law 557
Loop 88
Loop, digital 182 198
Lower limit see “Semi-continuity”
Lower skeleton 451—453
Lung, case study 26
Macro-instructions 374
Macrostructure 293 296
Magnifications see “Change of scale”
Mapping see “Transformation”
Marking 401—405 472—474
Markov processes 551—552 556
Mask corrections 49 (see also “Edge effects”)
Mathematical morphology see “Principles”
Matheron topology see “Hit or Miss topology”
Matheron topology, Matheron — Kendall theorem 547
Matheron topology, Matheron’s axioms 319—321
Maximum 445 589
Measurable function 115 322
Measurable transformation 84
Measurement see “Parameter”
Measures 114—115 119 283 437
Measures, estimation 250
Measuring mask 11 114 238 242
Medial axis 382—387
Median filtering 270 475—476
Metallic grains, case studies 247—248 252 406—409
Metallic grains, case studies, tesselations 524—530
Metallography case studies 364—365 409—411 458—460 482 499—502
Metrics, digital 188
Metrics, Hausdorff metric 73 82
Metrics, hexagonal 189
Metrics, metric space 72 90
Migration process 292
Miles — Lantuejoul correction 246—248 409
Milling of rocks, case study 27 523—524
Minimum 445 589
Minkowski addition see “Dilation”
Minkowski addition, substraction see “Erosion”
Minkowski dimension 147
Minkowski functionals 102—104 125 137 146 488 551
Minkowski functionals for functions 464—468
Minkowski functionals, estimation 235 244
Minkowski functionals, hexagonal 194
Minkowski functionals, measures 115 139
Minkowski functionals, reduced 255
Mode of operation 29 239
Model 25 577—583
Model of covariance 287—296
Model, random 236
Modelling, example of 26—28
Module 166
Module, affine module 169
Moments see “Average”
Moments of covariance see “Range”
Moments of size distributions 328—329 347—349 352 362 366 372 519 530
Monotone see “Increasing and Convergence”
Multiphased textures 271 503—508 560—561 563
Muscle fibres, case study 307—310
Neighbour analysis 406—409
Neighbourhood, digital 186
Neighbourhood, sampling 237 240
Neighbourhood, topological 66
Nested disks 130 148
Noise 271 282 312
Noise on covariance 271 282 312
Noise on size distribution 362
Norm for convex Euclidean sets 104
Norm, estimate of 255
Norm, regular model 160
Nugget effect see “Poisson points”
Octagonal grid 174
Octahedric grid 196
Open set (topological) 66
Open set (topological), interval 67
Opening and skeleton 377
Opening for functions 433 444
Opening, algebraic 56
Opening, circular 363
Opening, dodecagonal 364
Opening, linear 325 362
Opening, morphological 50—56 270 589
Opening, scaling table 366
Opening, size distributions 321 333—339 518
Opening, topological properties 86
Ordering relations 60 118
Orientation 227
Overlappings 405 581
Parameters, estimation for the covariance 280—283
Parameters, morphological 117 127—129 589
Parameters, specific 241 488 495 516—517
Parameters, topological 135
Particle 134 302
Particle, counting 158 233
Paths 88 182 198
Pattern recognition 584 (see also “Cytology”)
Perimeter 102
Perimeter and gradients 467
Perimeter and mean curvature 265
Perimeter for Euclidean convex sets 104
Perimeter, decomposition of 371
Perimeter, digital 183 191
Perimeter, digital estimates 220 222 228 422—423
Perimeter, perimetric measure 122 283
Periodic textures 271 288—289
Petrography, case studies 289
Petrography, case studies, clay 153—158
Petrography, case studies, porous media 339—344
Petrography, case studies, soils 506—508
Picture 426 432 434—437 451 589
Planar graphs 210
Planar graphs, representation 210 216
Point models 530—545 574—575
Poisson, functions 471
Poisson, lines 295 349 566—569 570—571
Poisson, points 211 315 484—485
Poisson, polyhedra 262 499 515—519 569—570
Poisson, slices 572—573
Poisson, tesselations 512—514
Powder, case study 353—356
Power spectrum 278
Prediction 576—579
Primitive vector 168
Principal directions 175—176
Principal directions in  195
Principal planes 195
Principles of mathematical morphology 6—15
Principles of mathematical morphology for erosion, opening 45—51
Principles of mathematical morphology for parameters 127—128
Principles of mathematical morphology for size distributions 334 357—358
Principles of mathematical morphology for thinnings 391
Probabilistic approach see “Randomness”
Probability of order two 277 295
Product of functions 436
Projection 105 115 270
Projection, average 258
Projection, digital 171 191
Pruning 392 397—399 407 411 419
Quantification see “Principles”
| Quench function 377 381 421 448
Random closed sets 545—553
Random closed sets, covariance of 287—296
Random closed sets, digitalization 216
Random closed sets, locally stationary 239
Random closed sets, size mappings 359
Random function 359 468—471
Random function, covariance of 307—309 313
Random variable 242—244 245 251 254 547 552
Randomness 29 231
RANGE 273 276 283 292 293 316
Regular model 141 146 160
Regular model and estimation 235
Regular model and skeleton 380
Regular model for functions 449
Regular model, digitalization 216 221
Regular model, particle extraction 402
Regularization 279 304
Relief grains 458 511 557—559
Representation 207—211
Representation, semi-continuity of 212
Rhombodocahedron 48 198—200 526 530
Rhombohedric grid 197
Rhombohedric grid, graphs 198
Ridge 440 452—455
Rolling ball transform 444
Rose of directions 283—286 467—468
Rose of directions, digitalization 223
Rotation, averaging 235 241
Rotation, digital 176 190 196 200
Rotation, invariance under 21
Rotation, sub-lattices 226 227
Run lengths see “Linear size distributions”
Ruts 440 453—456
Saddle 447 589
Sampling 217 231
Sampling, situations 232—235
Santalo formula 138
Santalo formula, kinematic densities 235
Section 258 (see also “Stereology average”)
Segmentation 413—416 437—439 456—463
Self similarity 151 (see also “Fractal sets”)
Semi-continuity for erosion and opening 86—87
Semi-continuity for functions 425—429
Semi-continuity for random sets 546
Semi-continuity for sets 78—81 589
Semi-continuity for thinnings 391
Semi-continuity of size distributions 334 358
Semi-continuity, principle of 12
Semi-Markov property 550—552
Sequential operations 393
Sequential operations, hexagonal sequences 395—400
SHAPE 321 336—339
Side 191 192
Sieving techniques 318
Sigma-algebra 65 469 546—547
Sink 445 450 456 589
Sinters, case study 503—506
Size distribution 270 (see also “Opening”)
Size distribution for functions 432—434
Size distribution, axioms 319—321
Size mappings 356—360
Skeleton 375
Skeleton for functions 451—456
Skeleton, digitalization 387—390
Skeleton, topology of 378—380
SKIZ 385—387
Skiz, digital 397
Smears see “Cytology”
Smoothing 418
Specific parameters see “Parameters”
Spherical particles see “Balls”
Square, graphs 180
Square, grid 174 419
Square, lattice 208
Stable random sets 549
Standard sequence 394
Star 322 325 347—350 472
Stationarity 236 275 578
Stationarity, local 238—239
Stationarity, test of 298 241
Steiner class 48 119 125
Steiner polyhedra 197
Steiner’s formula 111—114 131—132 138 139 240
Steiner’s formula, digital 193 203
Stereological parameters see “Minkowski functionals and Parameters”
Stereology 21 244 330—333
Stereology for balls 350—354
Stereology for Boolean model 489 555
Stereology for individuals 252—261
Stereology for Poisson model 513—514
Stereology, convex grains 264
Stereology, digital 191
Stochastic process see “Model and Random closed sets”
Structuring element 39 57—59
Structuring element, hexagonal 192
Summit 445 449 589
Sums of functions 434—435
Sup 430 431 433 436 443 450 452 464 469 471 477 589
Superimposed tesselations 563—565
Superimposition of scales 271
Superimposition of scales, examples of 300—307
Support function 117 122
Support of a function 115 426
Support of a measure 115
Support of a picture 426
Supporting half-spaces 117
Surface area 104
Surface area for Euclidean convex sets 104
Surface area, estimation 256
Surface area, specific 277
Symmetry 193 270
Symmetry by reflexion 441
Tangent count 142
Tangent count, tangent of the covariance 281
Tesselations 508—509 512—514
Tesselations, triple edge 574
Test of the Boolean model 495—502
Test of the Boolean model of stationarity 241 298
Tetrakaidecahedron 48 197 204—205 526 530
Texture 232 237
Texture analyser 23
Thalweigs see “Ruts”
Thick sections 105—108 496—498
Thickening 270 390 589
Thickening for functions 450—456
Thickening, examples of 407 411
Thickening, homotopic 392 395 419
Thinning 270 390 589
Thinning for functions 450—456
Thinning, examples of 407 411
Thinning, homotopic 392 395 419
Thresholding 270 433 457
Time evolution 235
Top hat transformation 436—437
topology 63—66 (see also “Hit or Miss”)
Topology, equivalent 90
Topology, Hausdorff 73
Topology, metric 72
Topology, order 70
Translation (compatibility and invariance under) and size mapping 357
Translation (compatibility and invariance under) for parameters 127
Translation (compatibility and invariance under) for transformations 8 45 239
Translation (compatibility and invariance under), digital 169
Transposed set 44
Trend analysis 422—423
Triple points 392 397
Twin flats model 520—523
Ultimate erosion 405 415 416
Umbra 270 428 441 450 469
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