Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

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



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Image Analysis and Mathematical Morphology

Автор: Serra J.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 620

Добавлена в каталог: 25.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Accumulation point      68
Adherent point      71
Algorithm      20—24
Alignments of points      541—543
Alternating capacity      548
Anamorphoses      435
Angular measures      119
Angularity      140 144 385
Angularity and size distribution      330 362—364
Anisotropy      271 283—286 301—304
Anisotropy, fast characterization      226
Antiextensivity      see also "Extensivity" 254 270 319
Area digital      35
Area digitalization      220
Area Euclidean      104
Area weighted representation      210
Asymptote for fractal sets      150
Asymptote for the covariance      282
Automorphism      167
Average      254—262
Average infinite      263
Balls      262
Balls Boolean      499
Balls, covariance of      310
Balls, size distribution      350—352
Balls, volume of      124
Basis digital      168 175
Basis topological      67
Bezout's identity      168
Bias      245 248
Boole — Poisson model      565—566
Boolean disks      482 553
Boolean disks, pore size distributions      361
Boolean functions      469
Boolean sets      485—502 581
Boolean sets in one dimension      555
Borel sets      114
Boundary      13 69 142 151
Boundary digital      183 198 200 392
Boundary, genus of      135 199
Bounded set      219 236 244
Brownian motion trajectories      543—544
C-additivity      109 548 550
C-additivity and sup-additivity      465
Cauchy formula      104 137
Cauwe's model      28 520—524 577—579
Cells with nuclei, estimation      255
Change of scale (principle) and convexity      96—98
Change of scale (principle) and size distributions      334 357—358
Change of scale (principle) compatibility under      9 151
Change of scale (principle), digital      202
Channel      447 456
Choquet's theorem      242 548 565
Chord      see "Linear size distribution"
Circularity factor      336—339
Clay soils, case study      506—508
Clay, case study      153—158
Closed set, topological      66
Closing algebraic      56
Closing and convex hull      98—100
Closing for function      433 444
Closing morphological      50—56 270 589
Closing pseudo      418
Closing scaling table      366
Closing, size distribution      336
Closing, topological properties      86
Clustered point model      535—537 543—544
Clusters      271 300 308
Coke, case study      499—502
Compact sets      73
Compactness      358
Compactness, locally compact space      71
Complementation      270 430
Complementation duality, w.r.t.      43 51 391 588—589
Conditional bisector      383—385
Conditional operations      393—394
Connected component      182
Connected component simply      182 193
Connected component, extraction      41 401—405
Connectivity      see also "Connected component" 88—89 433
Connectivity digital      182 198
Connectivity number      133—136 138 143
Connectivity number for Boolean model      211 492—494 557
Connectivity number for functions      467
Connectivity number, digitalization      220
Connectivity number, euclidean convex sets      104
Connectivity number, regular model      145—146 160
Consecutive points      171
Continuity      69
Continuity for the Hit or Miss topology      76 86
Continuity in regular model      146
Continuity of the skiz      387
Continuity, continuous functionals      109
contour      184
Contrast descriptors      see "Segmentation"
Convergence      see also "Continuity monotonic sequential" 14 70 77 81 88 214—215 426
Convex hull      98
Convex hull and skeleton      380
Convex hull, digital      42 171 416—418
Convex hull, digitalization      218 392
Convex polyhedra      108
Convex ring      133 193
Convex ring for functions      464-466
Convex ring, extension of      140—141 235
Convex ring, topology on      73
Convex sets and ordering relations      126
Convex sets and symmetry      126
Convex sets digital      171
Convex sets, average sections      264
Convex sets, digitalization      218
Convex sets, isotropic and digital      177 188
Convex sets, primary grains      489—491
Convex sets, random      548
Convex sets, size distribution      346—350
Convexity for functions      464—466 472
Convexity numbers      140—143 159
Convexity numbers in $Z^{3}$      204
Convexity numbers, digitalization      372
Convolution product      280 435
Conway's game      270 421
Correspondence analysis      342
Coulter counting      318
Counting logics      see also "Connectivity number" 201 204
Counts of overlapping particles      581
Covariance exponential      314
Covariance for Boolean sets      487
Covariance isotropic      313
Covariance measure      532 571
Covariance rectangular      276 312 314
Covariance, Poisson polyhedra      514
Covariance, Poisson slices      572
Covariogram      273
Covering representation      209 220 402
criteria      20—24
Crofton formula      104 137
Crofton formula digital      193 194
Crofton formula for thick sections      105
Crofton formula, digitalization      221
cube      48
Cube-octahedron      206 443
Cubic grid      196 204 557
Curvature      125 219 388
Curvature mean      160 265
Curvature, distribution of radii of      370—372
Curvature, regular model      146 224
Cytology, case studies      22—23 403—404 410—415 462—463
Dead leaves model      508—511
Defect lines      409—411
Definition field      237 245
Deterministic approach      236 272
Differences, function      434 436—437 444 472—473
Differences, set      376 389 390 407 416 449—450
Digital polygons      204
Digitalization      65 212 399 434
Digitalization for functions      449
Digitalization of the skeleton      387
Dilation      43—49 270 589
Dilation and convexity      96 102 172
Dilation functions      431 441 471 477
Dilation hexagonal      192 193
Dilation skeleton      377
Dilation, Steiner formula for      111
Dilation, topological properties      85—88 91
Dilution model      315
Dirac measure      115 437
Discrete Boolean model      554
disks      see also "Balls"
Disks, intercepts of      224
Disks, maximum      375
Disks, size distributions      350
Displacements      270
Displacements digital      169
Displacements, invariance under      109
Distance      see also "Metric"
Distance, pseudo distance      90 190
divides      446—447 456 589
Dodecagon      203
Dodecagon opening      364
Dodecagon perimeter      423
Dodecagon, convex hull      418
Dodecagon, dodecagonal grid      174
Doublets of points      538
Downstream      382
Duality w.r.t. complementation      588—589
EDGE      173 191
Edge corrections      233 409
Eight-connected graphs      182 184 201
Electron microscopy, case study      458—460
Embryonic ovary, case study      253 296—300
end points      392
Enhancement      476
Ergodicity      236 578
Erosion      39 43—49 62 248—249 270 589
Erosion for functions      431 441—444 471 477
Erosion linear      323—325
Erosion vhexagonal      192
Erosion, convexity      96 172
Erosion, parametrization using      381
Erosion, skeleton      377
Erosion, Steiner formula for      112
Erosion, topological properties      85—88 91
Estimator      242
Estimator of the covariance parameters      280—283
Estimator, asymptotically unbiased      245
Euler relation      185 210 229
Euler — Poincare constant      see "Connectivity number"
Extensivity      52 270
Extensivity, lack of      421
Falsifying experiments      577
Ferret's diameter      392
Filtering      474—476
Forest structure, case studies      483 538—539
Fourier transform      273 434
Fractal sets      147 152 311 543—544 550
Fractal sets, digitalization      215 421
Fractures in steel, case study      458—461
Fuzzy sets      425
Generating function      534
Geological case studies, calcite migration      290—294
Geological case studies, faults orientation      285
Geological case studies, sedimentary layer structure      304—307
Germ models      552
Global parameters      127
Global parameters, approach      232 409
Global parameters, covariance      272
Golay alphabet      392
Gradients      437—441 457—461 467
graphs      see also "Square Hexagonal Eight-connected"
Graphs digital      179 185 201
Graphs in $Z^{3}$      197
Grey tone function      426 589
Grids      172—174
Grids in $Z^{3}$      196
Grids, invariance      176
Hadwiger's theorem      109 550
Hard core point model      540—541
Heuristics      579—583
Hexagonal graphs      181
Hexagonal grid      174 348
Hexagonal lattice      208
Hexagonal prism      48
Hexagonal stereology      191—195
Hexagonal thinnings      392—403
Hierarchical models      561—563
Hills      447 456 589
Hit or Miss topology      75—85 429
Hit or Miss transformation      39 270 390
Hit or Miss transformation for functions      450
Hit or Miss transformation, topological properties      85—88
hole      183 185
Hole effect      290 313
Homeomorphism      69
Homogeneity      109 128 549
Homothetics      see "Change of scale"
Homotopy      see also "Thinning" 270 589
Homotopy digital      187 198 203 420
Homotopy for functions      445—449
Homotopy for regular model      144
Homotopy, digitalization      216 419
Homotopy, homotopic transformations      89
Human perception      586
Hyperplanes digital      168
Hyperplanes, parallel      170
Idempotence      52 270 321 394 588
Increasing transformations      13 48 52 55 270 319
Increasing transformations, digitability      214
Increasing transformations, functionals      109
Indicator function      128 272—275 425 486
Individual approach      232 407
Individual, estimation of      245 247 249 257—261 264
Individual, number of      254 260
Individual, size distribution      344—346 367 368
Induced grains      see "Stereology"
inf      430 431 433 436 443 450 452 471 477 589
Infinite divisibility      484 549
Integral geometry      102 255 550
Intercepts      see also "Linear size distribution"
Intercepts digital      171
Intercepts of a disk      224
Intercepts, number of      35 284
Interior      68
Interior, empty interior      109
Isolated point      68 392
Isolated primary grains      553
Isotropy      see also "Minkowski functionals" 544 578
Johnson — Mehl tesselation      527—529
Jordan theorem      88 184
Kriging      243
Laplace transform      288 534
Lattice      208
Lattice representation      208
Lattice translation      225
Lattice, sub-lattices and rotations      226
Law of the first contact      436 491
Least squares      281 284
Lebesgue measure      114
length measurement      see also "Crofton formula" 422—423
LIMIT      70
Linear size distribution      323—332 488—491 509 557 573
Linear size distribution digital      37
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2022
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте