Tensors in Image Processing and Computer Vision (eBook)

Santiago Aja-Fernández, Rodrigo de Luis Garcia, Dacheng Tao, Xuelong Li (Herausgeber)

eBook Download: PDF

2009 | 2009
IX, 470 Seiten
Springer London (Verlag)
978-1-84882-299-3 (ISBN)

Infos

Tensor signal processing is an emerging field with important applications to computer vision and image processing.

This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing.

This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.

Inhalt

Preface 5
Contents 7
A Review of Tensors and Tensor Signal Processing 10
1 Introduction 11
2 Tensor Definition 11
3 Example of Tensors in Mathematics 12
4 Example of Tensors in Physics and Engineering 17
5 Tensors Usage in Medical Imaging 20
6 Tensors Usage in Computer Vision 29
7 Conclusion 38
References 39
Part I Tensors and Tensor Field Processing 42
Segmentation of Tensor Fields: Recent Advances and Perspectives 43
1 Introduction 43
2 Tensors in Image Processing 44
3 Scalar Diffusion and Anisotropy Measures 47
4 Tensor Dissimilarity Measures 50
5 Tensor Field Segmentation Techniques 55
6 Summary 59
References 60
A Variational Approach to the Registration of Tensor- Valued Images 67
1 Introduction 67
2 The Variational Model 69
3 Experiments 75
4 Summary and Outlook 82
References 84
Quality Assessment of Tensor Images 86
1 Introduction 86
2 Background on Quality Assessment in Image Processing 88
3 Background on Tensor Images 91
4 Application of Quality Measures to Tensor Images 93
5 Experiments 98
6 Discussion 106
7 Conclusions 108
References 109
Algorithms for Nonnegative Tensor Factorization 111
1 Introduction 112
2 Formulating Nonnegative Tensor Factorizations 113
3 Solving the Optimization Problems Using Multiplicative Update Rules 118
4 Supervised Nonnegative Tensor Factorization 123
5 Applications of Nonnegative Tensor Factorizationss 125
6 Conclusions and Discussion 128
References 129
PDE-based Morphology for Matrix Fields: Numerical Solution Schemes 131
1 Introduction 132
2 Morphology for Grey Scale Images 133
3 Ordering Based Morphology for Matrix Fields 140
4 PDE-based morphology for Matrix Fields 144
5 Experimental Comparison of the Numerical Schemes 146
6 Conclusion 150
References 150
Part II Tensors in Image Processing 157
Spherical Tensor Calculus for Local Adaptive Filtering 158
1 Introduction 158
2 Spherical Tensor Analysis 161
3 Tensorial Harmonic Expansion 166
4 Local Adaptive Filtering with Tensorial Harmonics 171
5 Spherical Tensor Derivatives 174
6 local adaptive filtering with STDs 177
7 Conclusion 180
Appendix 181
References 182
On Geometric Transformations of Local Structure Tensors 184
1 Introduction 184
2 Background 185
3 Tensor Transformations 186
4 Local Structure Tensor Fields 188
5 Local Structure Analysis 191
6 Experiments 194
7 Results 195
8 Summary 197
References 197
Part III Tensors in Computer Vision 199
Multi-View Matching Tensors from Lines for General Camera Models 200
1 Introduction 200
2 Plücker Coordinates 202
3 Lines in Space 203
4 Multi-Focal Tensors from Lines 204
5 Constrained Camera Models 207
6 Experimental Results 212
7 Conclusions 213
Acknowledgements 214
References 214
Binocular Full-Body Pose Recognition and Orientation Inference Using Multilinear Analysis 218
1 Introduction 218
2 Overview of the Proposed Approach 220
3 Theoretical Background 221
4 Multilinear Analysis of Dance Pose Images 225
5 SVM-based Pose Recognition Using Pose Vectors 228
6 Body Orientation Estimation Using Orientation Vector through Manifold Learning and Nonlinear Minimization 230
7 Experimental Results 232
8 Conclusions and FutureWork 237
References 238
Applications of Multiview Tensors in Higher Dimensions 240
1 Introduction 241
2 Notation and Background Material 242
3 Higher Dimensional Spaces As Frameworks For Some Dynamic And Segmented Scenes 243
4 Multiview Tensors in Higher Dimension 244
5 Algorithms 246
6 Critical Configurations and Their Loci 248
7 Examples of Critical Loci for Projective Reconstruction 254
8 Instability Results 256
References 262
Constraints for the Trifocal Tensor 264
1 Introduction 264
2 The Trifocal Tensor 265
3 Constraints via Group Theory 267
4 Constraints via Geometry 269
5 A Minimal Set of Constraints 270
References 271
Part IV Diffusion Tensor Imaging and Medical Applications 273
Review of Techniques for Registration of Diffusion Tensor Imaging 274
1 Introduction 274
2 Registration of DT-MRI 276
3 Review of DT-MRI registration Algorithms 279
4 Similarity Measures 284
5 Diffusion Tensor Reorientation 287
6 Performance Evaluation 290
7 Discussion and Conclusions 292
Appendix. Scalar Measures of the Diffusion 294
References 296
Practical and Intuitive Basis for Tensor Field Processing with Invariant Gradients and Rotation Tangents 299
1 Introduction 299
2 Mathematical Background 300
3 Conceptual Overview 302
4 Invariant Gradients 303
5 Rotation Tangents 305
6 Example Application: Edge Detection 306
7 Other Applications 311
8 Discussion 311
References 312
From Second to Higher Order Tensors in Diffusion- MRI 315
1 Introduction 315
2 Principles of Diffusion MRI 316
3 Higher Order Tensors in D-MRI 324
4 Positivity Constraints 328
5 Conclusion 332
References 333
DT-MRI Connectivity and/or Tractography?: Two New Algorithms 335
1 Introduction 336
2 Connectivity or Tractography? 338
3 Lattice-of-Springs (LoS) 339
4 Split and Merge Tractography (SMT) 345
5 Concluding Remarks 349
References 351
Strain Rate Tensor Estimation in Cine Cardiac MRI Based on Elastic Image Registration 354
1 Introduction 354
2 Strain Tensor Definition 356
3 MRI Modalities to Estimate Strain and Strain Rate Tensor 358
4 Registration Methods 360
5 Phantom Design 362
6 Consistency Checking 364
7 Visualization 368
8 Real Data Results 370
9 Conclusion 375
References 376
Strain Tensor Elastography: 2D and 3D Visualizations 379
1 Introduction 379
2 Background 380
3 Strain Tensor Elastography (STE) 385
4 Experiments 389
5 2D Strain Tensor Elastography 390
6 3D Strain Tensor Elastography 392
7 Conclusions 397
References 399
Part V Storage, Visualization and Interfaces 402
Similar Tensor Arrays – A Framework for Storage of Tensor Array Data 403
1 Introduction 404
2 RelatedWork 405
3 Geometric Arrays 406
4 Scalar Arrays 407
5 Tensor Arrays 409
6 Examples of Use 413
7 Discussion 417
Appendix – Tensor Mathematics 417
References 423
User Interfaces to Interact with Tensor Fields 425
1 Introduction 425
2 Diffusion Tensor MRI 426
3 Visualization of Diffusion Tensor Fields 429
4 Command Line Interfaces 433
5 Graphical User Interfaces for Tensor Processing 435
6 Multimodal Interfaces for Tensor Processing 442
7 Discussion 444
8 Conclusions 446
References 447
T-flash: Tensor Visualization in Medical Studio 451
1 Introduction 451
2 The Tflash Tensor Glyph 452
3 Implementation as a MedicalStudio Component 455
4 Result 456
5 Conclusion 457
Appendix: Matlab code for Tflash 457
References 462
Index 463

Produkt-Details

• Erscheint lt. Verlag: 21.5.2009
• Reihe/Serie: Advances in Computer Vision and Pattern Recognition
• Reihe/Serie: Advances in Computer Vision and Pattern Recognition
• Zusatzinfo: IX, 470 p.
• Verlagsort: London
• Sprache: englisch
• Themenwelt: Informatik ► Grafik / Design ► Digitale Bildverarbeitung
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Schlagworte: 3D • Diffusion • DT-MRI • Image Processing • Image Registration • Multi-dimensional Signal Processing • Signal Processing • Tensor • Visualization
• ISBN-10: 1-84882-299-5 / 1848822995
• ISBN-13: 978-1-84882-299-3 / 9781848822993