Mathematical morphology and its applications to signal and image processing, 14 conf., ISMM 2019

Preface......Page 6
Organization......Page 7
Contents......Page 11
Theory......Page 15
 1 Introduction......Page 16
 2 Background: Morphology on Flat Lattices......Page 17
 3 Weighted Lattices......Page 18
 4 Vector and Signal Operators on Weighted Lattices......Page 20
 5 Tropical Geometry and CWL Generalizations......Page 23
  6.1 Solving Max- Equations......Page 25
  6.2 Regression for Optimal Fitting Tropical Lines to Data......Page 26
 References......Page 27
 1 Introduction......Page 29
  2.1 Mathematical Morphology Based on Structuring Elements......Page 30
  2.3 Monoid Structure......Page 31
  3.1 Introducing Neighborhoods Systems......Page 32
  3.3 Monoid Structure......Page 34
  3.4 Usual Properties: Towards Filters......Page 36
 4 Application: Morpho-Logic......Page 37
  4.1 Neighborhood Modal Logic......Page 38
  4.2 Topological Modal Logic......Page 39
 References......Page 40
 1 Introduction......Page 42
 2 Preliminaries......Page 43
 3 Heat Semigroup and Heat Kernel on Ultrametric Spaces......Page 44
 4 Laplacian on an Ultrametric Space......Page 47
 5 Laplace Operator on a Discrete Ultrametric Space......Page 49
 6 Application to Ultrametric Image Processing......Page 50
 7 Conclusions and Perspectives......Page 52
 References......Page 53
 1 Introduction......Page 54
  2.1 Logarithmic Image Processing......Page 56
  2.2 The LIP-multiplicative Asplund's Metric......Page 57
  3.1 General Expression of the Map of LIP-additive Asplund's Distances......Page 59
  3.2 Link Between the Maps of Distances (and the Metrics)......Page 60
 4 Illustration......Page 62
 References......Page 64
Discrete Topology and Tomography......Page 67
 1 Introduction......Page 68
 2 Mathematical Background......Page 69
  2.1 Pairing by Dynamics......Page 70
 3 Pairings by Dynamics and by Persistence are Equivalent in 1D......Page 71
 4 Conclusion......Page 77
 References......Page 78
  1.1 Context, Problem and Related Work......Page 80
 2 Basic Notions......Page 81
  3.1 Overview of the Approach......Page 82
  3.3 General Rules for Dual Mesh Generation......Page 83
  3.4 Generation of Dual Cells in Particular Cases......Page 84
  3.5 Handling Mixed Regions......Page 85
  3.7 Topological Guarantees......Page 89
  3.8 Post-processing......Page 90
  4.1 Application on Planar Meshes......Page 91
  4.2 Application on Surfaces......Page 92
 References......Page 93
 1 Introduction......Page 95
 2 Background......Page 96
 3 Topological Mapper for 3D Images......Page 97
  3.1 Structuring Element......Page 98
  3.3 Filtering......Page 99
  3.6 Implementation......Page 101
  4.2 z-filter......Page 102
 5 Discussion......Page 103
 References......Page 104
 1 Introduction......Page 107
 2 Definitions and Known Results......Page 108
 3 Results......Page 113
 References......Page 117
Trees and Hierarchies......Page 119
 1 Introduction......Page 120
  2.1 Hierarchies of Partitions......Page 121
  2.2 Braids of Partitions......Page 123
  2.3 The h-Equivalence as Starting Point to Compose a Braid......Page 124
 3 The Braid Construction Procedure......Page 125
 4 A Quick Look into the Braid Structure......Page 128
 5 Conclusion......Page 130
 References......Page 131
 1 Introduction......Page 133
  2.1 Hierarchies of Partitions......Page 134
  2.2 Graphs, Connected Hierarchies and Saliency Maps......Page 135
  2.3 Hierarchies of Minimum Spanning Forests and Watersheds......Page 136
  3.1 Binary Partition Hierarchies (by Altitude Ordering)......Page 138
  3.2 Watersheding Operator......Page 139
 4 Discussions and Perspectives......Page 142
 References......Page 144
 1 Introduction......Page 146
  2.2 Graphs, Connected Hierarchies and Saliency Maps......Page 148
  2.3 Hierarchies of Minimum Spanning Forests and Watersheds......Page 149
  3.1 Binary Partition Hierarchies (by Altitude Ordering)......Page 151
  3.2 Finding Probabilities of Hierarchical Watersheds......Page 152
  3.3 Most Probable Hierarchical Watersheds......Page 154
 References......Page 157
 1 Introduction......Page 159
 2 Background......Page 160
  3.1 Simple Attributes......Page 163
  3.2 Statistical Measures of Clusters of Nodes......Page 165
  4.1 Text Extraction......Page 166
  4.2 Computational Complexity and Time Consumption......Page 167
 References......Page 169
 1 Introduction......Page 171
  2.1 Definition and Properties of the Tree of Shapes......Page 172
  2.3 Quads......Page 174
  3.2 Counting Bit-Quads in Tree of Shapes Using Only Input Image Pixels......Page 176
  4.1 Connected Filter......Page 179
  4.2 Execution Time......Page 180
 References......Page 181
Multivariate Morphology......Page 183
 1 Introduction......Page 184
  2.1 Theoretical Background of the Model......Page 186
  2.2 Analysis......Page 187
  2.3 Exposition on the Algorithm......Page 188
 3 Experiments......Page 189
 4 Summary and Conclusion......Page 193
 References......Page 194
 1 Introduction......Page 196
 2 Mathematical Morphology......Page 198
  3.1 CP Decomposition......Page 199
  3.2 High-Order Singular Value Decomposition (HOSVD)......Page 201
  3.3 Alternating Optimization-Alternating Direction Method of Multipliers (AO-ADMM)......Page 202
  4.3 Results and Discussion......Page 204
 References......Page 207
 1 Introduction......Page 209
 3 From Hyperspectral Image to Matrix Field and Back......Page 211
  3.1 Vector Data to Matrix Field......Page 212
  3.2 Matrix Field to Vector Data: Approximate Inverse of......Page 214
  4.2 Continuous Morphology: Matrix-Valued Solution Scheme......Page 215
 5 Numerical Issues and Experiments......Page 216
 References......Page 219
 1 Introduction......Page 222
  2.1 Trees for Morphological Connected Openings and Closings......Page 223
  2.2 Connected Openings and Closings for Multi-band Images......Page 224
  3.1 Requirements for a Multivariate Component Tree......Page 226
  3.2 Multivariate Component Tree Construction......Page 227
 5 Conclusion......Page 232
 References......Page 233
 1 Introduction......Page 235
 2 Mathematical Morphology for Multivalued Images......Page 237
 3 Reduced Orderings......Page 238
 4 Approximation of h-Increasing Operators......Page 240
  4.1 -Morphological Operator......Page 241
  4.2 -Morphological Operator......Page 242
  4.3 Computational Experiments......Page 243
 5 Concluding Remarks......Page 245
 References......Page 246
Computational Morphology......Page 248
 1 Introduction......Page 249
  2.1 Intrinsic Volumes Estimated Based on 3D Binary Images......Page 250
  2.4 Sub-pixel Precise Euclidean Distance Transform......Page 251
 3 Intrinsic Volumes on Sub-pixel EDT Images for Refined Erosion Dilation Analysis......Page 252
  4.1 Nano-Porous ZrO2 and Al2O3 Ceramics......Page 253
  4.2 Ceramic Foams......Page 256
 5 Discussion......Page 259
 References......Page 260
 1 Introduction......Page 262
  2.1 Definitions......Page 263
  2.2 Data Structure......Page 264
  2.3 The –Tree Flooding Algorithm......Page 265
 3 The Tree Size Estimation......Page 267
 4 Experiments......Page 268
  4.1 TSE Performance......Page 269
 References......Page 272
 1 Introduction......Page 274
 2 The Representation of -Tree and Chaining Effect......Page 275
 3 The Contrast-Based -Tree......Page 276
 4 The Odd Gabor Filter Based -Tree......Page 277
  5.1 Segmentation Results on Synthetic Images......Page 279
  5.2 Segmentation Results on Remote Sensing Images......Page 282
 6 Conclusions......Page 284
 References......Page 285
 1 Introduction......Page 287
 2 Basic Concepts of Connectivity and Filtering......Page 289
 3 Attribute-Space Connectivity......Page 290
  3.1 Width-Based Attributes......Page 293
  3.2 Orientation Attributes......Page 294
 4 Connected Components Analysis, Higher-Dimensional Attributes and Filtering......Page 295
 5 Discussion......Page 297
 References......Page 299
Machine Learning......Page 301
 1 Introduction......Page 302
 2 Theoretical Background......Page 303
 3 Ultimate Levelings......Page 304
 4 Strategy to Filter Undesirable Residues Based on Machine Learning......Page 306
  4.1 Selecting Disjoint Residual Regions......Page 308
 5 Results and Experiments......Page 309
 6 Conclusion......Page 312
 References......Page 313
 1 Introduction......Page 315
 2 Related Work......Page 316
  3.1 Morphological Perceptron......Page 317
  3.3 Universal Function Approximator Property......Page 318
 4 Experiments......Page 319
  4.1 Filter Selection Property......Page 320
  4.2 Application to Model Pruning......Page 323
 5 Conclusions and Future Work......Page 325
 References......Page 326
 1 Introduction......Page 328
  2.1 Non-negative Sparse Mathematical Morphology......Page 330
  2.2 Deep Auto-encoders Approaches......Page 331
 3 Proposed Model......Page 334
 4 Experiments......Page 335
 References......Page 338
Segmentation......Page 340
 1 Introduction......Page 341
  3.1 Weighted Graphs......Page 342
  3.2 The Flooding Distance......Page 343
  3.3 Floodings on Graphs......Page 344
  4.1 A Marker Based Segmentation Associated to the Minimum Spanning Forests of the Graph......Page 346
  4.2 The Topography of the Graph G(,nil)......Page 347
 5 Marker Based Segmentation of a Node Weighted Graph......Page 350
 6 Conclusion......Page 351
 References......Page 352
 1 Introduction......Page 354
 2 Algorithm......Page 356
  2.1 Region Growing......Page 357
  2.3 Refinement......Page 359
  3.1 Metrics......Page 360
  3.2 Result and Discussion......Page 362
 4 Conclusion......Page 363
 References......Page 364
 1 Introduction......Page 366
 2 Distance-Based Elementary Morphological Operators......Page 367
 3 Characterization of Distance-Based Morphological Operators......Page 369
 4 Statistics of Distance-Based Morphological Operators......Page 370
 5 Computational Experiment......Page 374
 6 Concluding Remarks......Page 376
 References......Page 377
 1 Introduction......Page 379
 2 Morphology on Irregularly Sampled Data......Page 380
  2.1 Dilations of Irregularly Sampled Signals......Page 381
 3 Irregular Morphology for Point Clouds......Page 383
 4 Application to Urban Point-Cloud Segmentation......Page 384
  4.2 Segmenting Facades......Page 385
  4.4 Segmenting Ground and Refining Labeling......Page 387
  4.6 Results......Page 388
 5 Discussion and Conclusions......Page 389
 References......Page 390
Applications in Engineering......Page 392
 1 Introduction......Page 393
  2.1 Mathematical Morphology on Point Clouds......Page 394
  2.2 Morphological Hierarchies on 3D Images......Page 395
  3.1 From Point Cloud to Voxel Grid......Page 396
  3.2 Attribute Filtering with the Max-Tree of Voxels......Page 397
  4.2 Experimental Setup......Page 399
 5 Conclusion......Page 402
 References......Page 403
 1 Introduction......Page 405
 2 Complementarity Preserving Scale Space......Page 407
  3.1 Boundary Morphology......Page 408
  3.2 Lipschitz Condition......Page 410
  3.3 Extrusion......Page 411
  3.4 Distance-Transform Based MM Implementation......Page 412
  3.5 MM Surfaces......Page 413
 4 Inexact Complementarity......Page 414
 5 Conclusion and Future Work......Page 415
 References......Page 416
 1 Introduction and Motivation......Page 417
 2 Related Work......Page 418
  3.1 Granulometries and Pattern Spectra......Page 419
  3.2 Component Trees......Page 420
 4 Dataset Description......Page 422
 5 Experiments and Results......Page 423
 6 Conclusions and Future Work......Page 427
 References......Page 428
 1 Introduction......Page 430
 2 Background......Page 431
 3 Proposed Contact Based Attribute Function......Page 433
  4.1 Datasets......Page 436
  4.3 Experimental Set-Up......Page 437
  5.2 Comparison Against Morphological Watershed......Page 438
  5.3 Evaluation of Unsupervised Hierarchies on Natural Grains......Page 439
 6 Conclusion......Page 440
 References......Page 441
 1 Introduction......Page 443
 2 Algorithm......Page 444
 3 Validation......Page 447
  4.1 Open Cell Aluminum Foam......Page 450
  4.2 Greenland Firn......Page 451
  4.3 Mice Livers......Page 453
 5 Discussion......Page 455
 References......Page 456
 1 Introduction......Page 458
  2.2 Geodesic Operators: Distance, Extremities and Diameter......Page 459
  2.3 Max-Tree......Page 461
 3 Finding Junction Regions......Page 463
 4 Results......Page 465
 References......Page 468
Applications in (Bio)medical Imaging......Page 470
 1 Introduction......Page 471
 2 Related Works......Page 472
  3.1 Theory......Page 473
  3.2 Application......Page 474
 4 Multilabel, Multiscale Topology-Controlled Deformation......Page 475
  4.2 Metrics......Page 476
  4.3 Initialization and Optimization Process......Page 477
 5 Experiments and Results......Page 478
 6 Conclusion......Page 480
 References......Page 481
 1 Introduction......Page 483
  2.1 MR Images and Preprocessing......Page 485
  2.2 Initial Partitioning: Waterpixels......Page 486
  2.4 Features for BPT Construction......Page 487
 3 Experiments and Results......Page 488
  3.1 Watervoxel Partition: Parameter Setting......Page 489
  3.2 Segmentation/BPT Evaluation......Page 490
 4 Conclusion and Perspective Works......Page 492
 References......Page 493
 1 Introduction......Page 496
 2 Swim Bladder Localization......Page 498
  2.2 Swim Bladder Segmentation......Page 499
 3 Swim Bladder Characterization......Page 502
  3.2 Morphological Descriptors......Page 503
  4.1 Experimental Setup......Page 504
  4.3 Classification Results and Discussion......Page 505
 References......Page 506
 1 Introduction......Page 508
 2 Tree of Shapes......Page 510
 3 Attribute Profiles and Pattern Spectra......Page 512
 4 Choice of the Attribute and of the Measure......Page 513
 5 Experiments......Page 516
 References......Page 518
 1 Introduction......Page 520
  2.1 2D Segmentation......Page 521
  2.2 3D Regularization......Page 522
  2.3 3D Individualization......Page 523
  3.1 Centroid Estimation in 2D......Page 524
  3.2 Centroid Estimation in 3D with Known Bead Radius......Page 525
  3.3 Centroid Estimation in 3D with Imprecise Bead Radius......Page 527
 4 Results on Simulations......Page 528
 5 Results on Real Data......Page 529
 References......Page 530
 1 Introduction......Page 532
 2 Methods......Page 534
  3.1 Combined Mathematical Morphology and Hilbert Transform for Accurate Nuclei Counting......Page 536
  3.2 HEDAR is Able to Accurately Extract Ellipse Parameters from Detected Ellipses......Page 537
  3.3 HEDAR is Able to Accurately Count Ellipses......Page 539
  3.4 Details of Benchmarking Data......Page 540
 4 Conclusions......Page 541
 References......Page 542
Author Index......Page 544