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Serra J. — Image Analysis and Mathematical Morphology
Serra J. — Image Analysis and Mathematical Morphology



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Íàçâàíèå: Image Analysis and Mathematical Morphology

Àâòîð: Serra J.

Àííîòàöèÿ:

Mathematical morphology was born in 1964 when G. Matheron was asked to investigate the relationships between the geometry of porous media and their permeabilities, and when at the same time, I was asked to quantify the petrography of iron ores, in order to predict their milling properties. This initial period (1964-1968) has resulted in a first body of theoretical notions (Hit or Miss transformations, openings and closings, Boolean models), and also in the first prototype of the texture analyser. It was also the time of the creation of the Centre de Morphologie Mathematique on the campus of the Paris School of Mines at Fontainebleau (France). Above all, the new group had found its own style, made of a symbiosis between theoretical research, applications and design of devices.
These have the following idea in common: the notion of a geometrical structure, or texture, is not purely objective. It does not exist in the phenomenon itself, nor in the observer, but somewhere in between the two. Mathematical morphology quantifies this intuition by introducing the concept of structuring elements. Chosen by the morphologist, they interact with the object under study, modifying its shape and reducing it to a sort of caricature which is more expressive than the actual initial phenomenon. The power of the approach, but also its difficulty, lies in this structural sorting. Indeed, the need for a general theory for the rules of deformations appeared soon. The method progressed as a result of an interchange between intellectual intuitions and practical demands coming from the applications. This finally lead to the content of this book. On the way, several researchers joined the initial team and constituted what is now called the "Fontainebleau School". Among them, we can quote J.C. Klein, P. Delfiner, H. Digabel, M. Gauthier, D. Jeulin, E. Kolomenski, Y. Sylvestre, Ch. Lantuejoul, F. Meyer and S. Beucher.
A new theory never appears by spontaneous generation. It starts from some initial knowledge and grows in a certain context. The family tree of mathematical morphology essentially comprises the two branches of integral geometry and geometrical probabilities, plus a few collateral ancestors (harmonic analysis, stochastic processes, algebraic topology). Apart from mathematical morphology, three other parallel branches may be considered as current descendants of the same tree. They are stereology, point processes and stochastic geometry as developed by D. G. Kendall's School at Cambridge. Stereology, unlike the other two, is oriented towards applications. The stereologists have succeeded in putting the major theorems of integral geometry into practice. Indeed their society regroups biologists and specialists of the material sciences whose mutual interest lies in the quantitative description of structures, principally at the microscopic scale.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1982

Êîëè÷åñòâî ñòðàíèö: 620

Äîáàâëåíà â êàòàëîã: 25.11.2014

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Linear size distribution, digitalization      360
Local approach      232 440
Local approach for the covariance      275
Local knowledge and mask corrections      49
Local knowledge example      406
Local knowledge for erosion      46 61
Local knowledge for parameters      128
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      see also "Semi-Markov property" 551—552 556
Mask corrections      see also "Edge effects" 49
Mathematical morphology      see "Principles"
Matheron topology      see "Hit or Miss topology"
Matheron — Kendall theorem      547
Matheron's axioms      319—321
Maximum      see also "Summit and Sup" 445 589
Measurable function      115 322
Measurable transformation      84
Measurement      see "Parameter"
Measures      see also "Minkowski" 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
Metallography case studies      see also "Metallic grains" 364—365 409—411 458—460 482 499—502
Metrics digital      188
Metrics hexagonal      189
Metrics, Hausdorff metric      73 82
Metrics, metric space      72 90
Migration process      292
Miles-Lantuejoul correction      246—248 409
Milling of rocks, case study      27 523—524
Minimum      see also "Sink and Inf" 445 589
Minkowski addition      see "Dilation"
Minkowski dimension      147
Minkowski functionals      102—104 125 137 146 488 551
Minkowski functionals for functions      464—468
Minkowski functionals hexagonal      194
Minkowski functionals, estimation      235 244
Minkowski functionals, measures      115 139
Minkowski functionals, reduced      255
Minkowski substraction      see "Erosion"
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 also "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 algebraic      56
Opening and skeleton      377
Opening circular      363
Opening for functions      433 444
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
Openingdodecagonal      364
Ordering relations      60 118
Orientation      227
Overlappings      405 581
Parameters morphological      117 127—129 589
Parameters specific      241 488 495 516—517
Parameters topological      135
Parameters, estimation for the covariance      280—283
Particle      see also "Connected component" 134 302
Particle counting      158 233
Paths      88 182 198
Pattern recognition      see also "Cytology" 584
Perimeter      102
Perimeter and gradients      467
Perimeter and mean curvature      265
Perimeter digital      183 191
Perimeter for Euclidean convex sets      104
Perimeter, decomposition of      371
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 $Z^{3}$      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 digitalization      216
Random closed sets, covariance of      287—296
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      see also "Stereology"
Section, average      258
Segmentation      413—416 437—439 456—463
Self similarity      see also "Fractal sets" 151
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      see also "Opening" 270
Size distribution for functions      432—434
Size distribution, axioms      319—321
Size mappings      356—360
Skeleton      375
Skeleton digitalization      387—390
Skeleton for functions      451—456
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      see also "Cauchy and Crofton formulae" 21 244 330—333
Stereology digital      191
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
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 estimation      256
Surface area for Euclidean convex sets      104
Surface area, specific      277
Symmetry      see also "Transposed set" 193 270
Symmetry by reflexion      441
Tangent count      142
Tangent count, tangent of the covariance      281
Tesselations      524-530
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 homotopic      392 395 419
Thickening, examples of      407 411
Thinning      270 390 589
Thinning for functions      450—456
Thinning homotopic      392 395 419
Thinning, examples of      407 411
Thresholding      270 433 457
Time evolution      235
Top hat transformation      436—437
topology      see also "Hit or Miss" 63—66
Topology equivalent      90
Topology Hausdorff      73
Topology metric      72
Topology order      70
Translation (compatibility and invariance under) digital      169
Translation and size mapping      357
Translation for parameters      127
Translation for transformations      8 45 239
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
Uniform distribution      see also "Poisson points" 234 251 253 262
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