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Tensors in Image Processing and Computer Vision

:	Santiago Aja-Fernández, Rodrigo de Luis Garcia, Dacheng Tao, Xuelong Li
:	Tensors in Image Processing and Computer Vision
:	Springer-Verlag
:	9781848822993
:	Advances in Computer Vision and Pattern Recognition
:	1
:	CHF 135.30
:

:	Anwendungs-Software
:	English

:	470
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	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