Scale Space and Variational Methods in Computer Vision: 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 – July 4, 2019, Proceedings

Preface......Page 7
Tribute to Mila Nikolova (1962–2018)......Page 8
Organization......Page 9
Contents......Page 11
3D Vision and Feature Analysis......Page 16
 1 Introduction......Page 17
  2.1 The CRONE Operator......Page 18
 3 The Harris-Laplace Detector......Page 19
 4 The Fractional Harris-Laplace Detector......Page 20
 5 Results......Page 21
  5.2 Boats2 Sequence......Page 22
 6 Discussion......Page 23
 References......Page 25
 1 Introduction......Page 27
  2.1 Microcanonical Models......Page 29
  2.2 Macrocanonical Models......Page 30
  2.3 Some Feature Examples......Page 32
  3.2 Sampling from Gibbs Measures......Page 33
 4 Experiments......Page 34
  4.1 Empirical Convergence of the Sampling Algorithm......Page 35
 5 Perspectives......Page 36
 References......Page 37
 1 Introduction......Page 39
 2 Preliminaries and Main Assumptions......Page 40
  3.1 Outlier Estimation......Page 41
  3.2 Step 2: Adaptive Regularization Using the Isoperimetric Loss (IPL)......Page 43
  4.1 Manifold Denoising......Page 46
  4.2 The RIPL Approach......Page 47
  4.3 Experiments with Real Data: Application to Motion Segmentation......Page 48
  4.4 Experiments with Real Data: Application with 3D Laser Scan Data......Page 49
 5 Discussion......Page 50
 References......Page 51
 1 Introduction......Page 52
  2.1 The Eikonal Equation......Page 53
  2.3 Fast Eikonal Solvers......Page 54
 3 Deep Eikonal Solver......Page 55
  3.1 Training the Local Solver......Page 56
  3.2 Deep Eikonal Solver for Cartesian Grids......Page 58
  4.1 Experimental Results......Page 59
 References......Page 62
 1 Introduction......Page 65
 2 Preliminaries......Page 66
 3 A Generic Splitting Strategy for Multi-view Stereo......Page 68
 4 Regularizers for Textureless Multi-view Stereopsis......Page 69
 5 Experimental Results......Page 72
 References......Page 76
Inpainting, Interpolation and Compression......Page 78
 1 Introduction......Page 79
 2 From Harmonic to Pseudodifferential Inpainting......Page 81
 3 Interpolation with Radial Basis Functions......Page 82
 4 Connecting both Worlds......Page 83
 5 One Numerical Algorithm for All Approaches......Page 84
 6 Experiments......Page 86
 7 Conclusions and Outlook......Page 88
 References......Page 89
 1 Introduction......Page 91
  2.1 Image Inpainting with PDEs......Page 92
  2.3 Optical Flow......Page 94
 3 Combining Optimal Masks with Flow Data......Page 95
  4.1 Methods Considered......Page 96
  4.3 Influence of the Optical Flow......Page 97
  4.4 Evaluation of the Reconstruction Error......Page 100
 References......Page 101
 1 Introduction......Page 104
 2 A Framework for Inpainting-Based Audio Compression......Page 106
 3 Localised Sample Optimisation with 1-D Inpainting......Page 109
 4 Experiments......Page 111
 5 Conclusions and Outlook......Page 113
 References......Page 114
 1 Introduction......Page 116
 2 Related Work......Page 117
 3 Statement of the Problem......Page 118
  3.2 Textural Reconstruction Energy......Page 119
  4.1 Motion Estimation......Page 120
  4.2 Structural Reconstruction......Page 121
  4.3 Shift Maps Estimation and Textural Reconstruction......Page 122
  5.1 Qualitative Results......Page 124
  5.2 Quantitative Results......Page 126
 References......Page 127
Inverse Problems in Imaging......Page 129
 1 Introduction......Page 130
 2 Sampled Tikhonov Methods for Linear Inverse Problems......Page 132
 3 Iterative Sampled Methods for Separable Nonlinear Inverse Problems......Page 133
 4 Numerical Results......Page 135
  4.1 Experiment 1: Comparing sn-slimTik to Variable Projection......Page 136
  4.2 Experiment 2: sn-slimTik for a Massive Problem......Page 137
 References......Page 140
 1 Introduction......Page 142
  1.1 Refitting......Page 143
  2.1 Properties of Bregman Divergence of ell12 Structured Regularizers......Page 144
  2.2 Bregman-Based Refitting......Page 145
 3 Refitting with Block Penalties......Page 146
  3.1 Desired Properties of Refitting Block Penalties......Page 147
  3.3 SD Block Penalty: The Best of Both Bregman Worlds......Page 148
  4.1 Biased Problem and Posterior Refitting......Page 149
  4.2 Joint-Refitting Algorithm......Page 150
 5 Results......Page 152
 6 Conclusion......Page 153
 References......Page 154
An Iteration Method for X-Ray CT Reconstruction from Variable-Truncation Projection Data......Page 155
 1 Introduction......Page 156
 2 Prior Knowledge of Background......Page 157
 3 CT Reconstruction Based on Sparse Representation......Page 159
  3.1 Determinations of r1t and r2t......Page 160
 4 Numerical Experiments......Page 161
 5 Conclusions and Future Work......Page 164
 References......Page 165
 1 Introduction......Page 167
  1.1 Previous Work......Page 168
 2 Our Method......Page 169
  2.1 An Iterative Algorithm......Page 170
  2.2 Approximation of L|x......Page 171
 3 Numerical Experiments......Page 172
  3.1 The Small Example......Page 174
  3.2 The Larger Example......Page 176
 References......Page 177
Optimization Methods in Imaging......Page 179
Time Discrete Geodesics in Deep Feature Spaces for Image Morphing......Page 180
 1 Introduction......Page 181
 2 Review of the Metamorphosis Model......Page 182
 3 Time Discrete Metamorphosis Model in Feature Space......Page 183
 4 Fully Discrete Metamorphosis Model in Feature Space......Page 185
 5 Numerical Optimization Using the iPALM Algorithm......Page 186
 6 Numerical Results......Page 189
 References......Page 191
 1 Introduction......Page 192
 2 Minimal Lipschitz Extensions and Approximations......Page 193
 3 Midrange Filters and -Harmonic Extensions......Page 197
 4 -Laplacians on Scalar-Valued Functions......Page 200
 References......Page 202
PDEs and Level-Set Methods......Page 205
 1 Introduction......Page 206
  2.1 The Convex-Hull-Stripping Median of Finite Sets......Page 208
  2.2 Continuous-Scale Limit......Page 209
 3 Experiments......Page 212
 References......Page 216
 1 Introduction......Page 218
  2.1 The Homogeneous Space M of Positions and Orientations......Page 220
  2.2 Total-Roto Translation Variation, Mean Curvature Flows on M......Page 222
  2.3 Gradient-Flow Formulations and Convergence......Page 223
  2.4 Numerics......Page 224
  3.1 TVF and MCF on R3 S2 for Denoising FODFs in DW-MRI......Page 225
  3.2 TVF and MCF on R2 S1 for 2D Image Enhancement/Denoising......Page 227
 References......Page 228
 1 Introduction......Page 231
  2.1 Preliminaries......Page 232
  2.2 Exact Convex Hull Model......Page 233
  2.3 The Algorithms for Proposed Models......Page 235
  3.1 Discretization Scheme......Page 236
  3.2 Initialization and Determination of Landmarks......Page 238
  4.1 Exact Convex Hull Model......Page 239
  4.2 Convex Hull Model for Outliers......Page 240
 References......Page 241
 1 Introduction......Page 243
 2 M-Smoothers, Mode and Partial Differential Equations......Page 245
 3 An L-stable Numerical Scheme for the PDE Limit......Page 249
 4 Experiments......Page 252
 5 Summary and Conclusions......Page 253
 References......Page 254
Registration and Reconstruction......Page 256
 1 Introduction......Page 257
 2 Registration Approaches for Multiple Images......Page 258
  2.2 Sequential Registration Approach for Multiple Images......Page 259
  2.4 Schatten q-norm Based Image Similarity Measure DS,q......Page 260
  2.6 Correlation Maximization of Normalized Features......Page 261
 3 Numerical Methods......Page 262
 4 Results......Page 263
 5 Discussion and Conclusions......Page 265
 References......Page 267
 1 Introduction......Page 269
  2.1 Mathematical Model and Notation......Page 271
  2.2 Joint Variational Model......Page 272
  2.3 Numerical Method: Optimisation Scheme......Page 274
 3 Numerical Experiments......Page 275
 References......Page 279
 1 Introduction......Page 281
 2 Mathematical Preliminaries......Page 282
  3.1 Rational-Order Pyramid Transform......Page 283
  3.2 Discretisation of Variational Method......Page 284
 4 Resolution Interpolation......Page 285
  5.2 Resolution Interpolation......Page 287
 6 Conclusions......Page 288
 References......Page 292
Scale-Space Methods......Page 294
 1 Introduction......Page 295
 2 Gradient Flows and Eigenfunctions......Page 296
 3 An Iterative Scheme to Compute Nonlinear Spectral Decompositions......Page 297
  3.2 The General Case......Page 299
  4.1 Numerical Computation of Extinction Profiles......Page 300
  4.3 Spectral Clustering with Extinction Profiles......Page 301
  4.4 Outlook: Advanced Clustering with Higher-Order Eigenfunctions......Page 304
 References......Page 305
 1 Introduction......Page 307
 2 Theoretical Results......Page 308
  2.1 Formalisation of Discrete Sparsification Scale-Spaces......Page 309
  2.2 Scale-Space Properties......Page 310
 3 Specific Aspects and Experiments......Page 312
 4 Conclusions and Future Work......Page 314
 References......Page 317
 1 Introduction......Page 319
  2.1 Eigenfunctions of the p-Laplacian......Page 321
 3 Analysis of Explicit Schemes for Shape Preserving Flows......Page 322
  3.1 Convergence Criterion for Adaptive Step Size......Page 323
  3.2 Stability Criterion for Fixed Step Size......Page 325
 4 Arbitrary Initial Conditions......Page 326
 5 Results and Conclusion......Page 328
 References......Page 330
 1 Introduction......Page 332
 2 The Quasi Quadrature Measure over a 1-D Signal......Page 333
 3 Oriented Quasi Quadrature Modelling of Complex Cells......Page 336
 4 Hierarchies of Oriented Quasi Quadrature Measures......Page 338
 5 Application to Texture Analysis......Page 340
 6 Summary and Discussion......Page 341
 References......Page 342
 1 Introduction......Page 345
 2 Semi-discrete Optimal Transport......Page 347
  3.1 Multi-scale Semi-discrete Optimal Transport......Page 348
  3.2 Multi-layer Transport Map......Page 349
  4.2 Texture Synthesis......Page 352
 5 Discussion and Conclusion......Page 355
 References......Page 356
Segmentation and Labeling......Page 358
 1 Introduction......Page 359
  2.1 Conventional Affinity Matrix......Page 361
  2.2 Full-Range Affinity Matrix......Page 362
 3 Results......Page 365
 4 Conclusion......Page 369
 References......Page 370
 1 Introduction......Page 371
 2 Derivation of the Model......Page 373
 3 First Variations and Optimisation......Page 375
 4 Experimental Validation......Page 377
 5 Conclusion......Page 381
 References......Page 382
 1 Introduction......Page 383
  2.1 Review on Lattice Metric Space......Page 384
  2.2 Properties in Relation to Grain Defect Detection......Page 386
 3 Lattice Clustering Algorithm......Page 387
 4 Numerical Experiments and Discussion......Page 388
 References......Page 393
 1 Introduction......Page 395
  2.1 Assignment Flow......Page 397
  3.1 Parameter Estimation by Trajectory Optimization......Page 399
  3.2 Parameter Estimation: Continuous Approach......Page 400
  3.3 Parameter Estimation: Discrete Approach......Page 401
  3.5 Parameter Estimation Algorithm......Page 402
  3.6 Parameter Prediction......Page 403
 4 Experiments......Page 404
 References......Page 406
 1 Introduction......Page 408
 2 Proposed Method......Page 410
 3 Experiments......Page 414
 4 Conclusion......Page 417
 References......Page 418
 1 Introduction......Page 421
  2.1 Minimizing the Contour Energy Using Phase Field......Page 422
  3.1 Approximate System Energy......Page 423
  3.2 Cubic Ansatz......Page 424
  3.3 The Motion of the Level Sets......Page 425
 4 Phase Field Model for Reinitialization Purpose......Page 426
  4.1 Determining Weights......Page 427
  5.1 Stability Tests: Comparing to the Ginzburg-Landau Model......Page 428
  5.2 Comparing to the Reaction-Diffusion Model......Page 429
 References......Page 432
 1 Introduction......Page 434
 2 Assignment Flow: Supervised Labeling......Page 435
  3.1 Rationale......Page 437
  3.2 Computational Approach......Page 438
  3.3 Spatially Regularized Optimal Transport......Page 440
  4.1 Nonnegative Matrix Factorization (NMF)......Page 441
 5 Experiments......Page 442
 References......Page 445
Variational Methods......Page 447
 1 Introduction......Page 448
 2 Related Work......Page 449
 3 Variational Methods for Aorta Centerline Smoothing......Page 450
 4 Variational Methods for Aorta Centerline Registration......Page 452
 5 Experimental Setup......Page 453
 References......Page 458
 1 Introduction......Page 460
  2.2 Properties of the Equations......Page 462
  2.3 Connection to Image Processing Models......Page 463
  3.1 A Geometric Model of Color Perception......Page 465
  3.2 Connection to Image Processing Models......Page 466
  4.1 A New Operator and Its Connections to Existing Layers......Page 467
  4.2 Learning the Parameters of the Operator......Page 468
  4.3 Experiments......Page 469
 References......Page 470
 1 Introduction......Page 473
 2 Orientation-Independent Variational Models......Page 474
 3 A Cortical-Inspired Model......Page 475
  3.1 Functional Lifting......Page 476
  3.2 WC-Type Mean Field Modelling......Page 477
  3.3 Discretisation via Gradient Descent......Page 478
 4 Numerical Results......Page 479
  4.1 Grating Induction with Oriented Relative Background......Page 480
  4.2 Poggendorff Illusion......Page 481
 References......Page 483
 1 Introduction......Page 486
 2 Primal and Dual Formulations......Page 488
 3 Basic Properties and Relationship with Other `3́9`42`\"̇613A``45`47`\"603ATV-type Regularizers......Page 489
 4 Numerical Experiments......Page 491
  4.1 1D Experiments......Page 492
  4.2 2D Experiments......Page 494
 References......Page 497
 1 Introduction......Page 499
 2 Image Formation Modelling......Page 500
 4 Optimization Model NCNS for SMLM Problem......Page 501
  4.1 Solving the Minimization Step......Page 503
 5 Numerical Experiments......Page 505
  5.1 Performance Evaluation......Page 506
 References......Page 510
 1 Introduction......Page 511
  2.1 PCR Functions......Page 512
  2.2 The 1-Anisotropic ROF Model......Page 515
 3 The Averaging Operator AG......Page 517
 4 Conclusion......Page 521
 References......Page 522
 1 Introduction......Page 523
  2.1 The Directional Information......Page 525
  2.2 The Regulariser......Page 526
  2.3 Connections to Optical Flow......Page 527
  3.1 Discretisation of Derivative Operators and Vector Fields......Page 528
  4.1 Selection of Parameters......Page 530
  4.3 Discussion of Results......Page 531
 References......Page 534
 1 Introduction......Page 536
 2 A CNN to Compute a Statistical Distribution of Color......Page 538
 3 A Variational Model for Image Colorization with Channels Coupling......Page 539
 4 Joining Total Variation Model with CNN......Page 541
 5 Numerical Results......Page 543
 References......Page 546
 1 Introduction......Page 548
 2 Preliminaries......Page 549
 3 Model......Page 551
 4 Optimization Approach......Page 554
 References......Page 558
 1 Introduction......Page 560
  2.1 Continuous Formulation......Page 563
  2.2 Connection to the Discretization-First Approach [15]......Page 565
  2.3 Numerical Aspects......Page 567
 3 Numerical Results......Page 568
 4 Conclusion......Page 570
 References......Page 571
Author Index......Page 573