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Visualization and Processing of Tensor Fields Advances and Perspectives

:	Gerald Farin, Hans-Christian Hege, David Hoffman, Christopher R. Johnson, Konrad Polthier
:	David H. Laidlaw, Joachim Weickert
:	Visualization and Processing of Tensor Fields Advances and Perspectives
:	Springer-Verlag
:	9783540883784
:	1
:	CHF 85.50
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	376
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This book provides researchers an inspirational look at how to process and visualize complicated 2D and 3D images known as tensor fields. With numerous color figures, it details both the underlying mathematics and the applications of tensor fields.

	Preface	6
	Contents	7
	List of Contributors	10
	Part I Models for Diffusion MRI	15
	Modelling, Fitting and Sampling in Diffusion MRI	16
	1 Introduction	16
	2 Background	17
	3 Methods	19
	4 Experiments and Results	26
	5 Discussion	29
	References	29
	Tensors, Polynomials and Models for Directional Data	34
	1 Introduction	34
	2 Tensors, Symmetric Tensors and Multivariate Polynomials	34
	3 Signals and Directional Signals	41
	4 Summary and Conclusions	48
	Acknowledgments	48
	References	48
	A Mixture of Wisharts (MOW) Model for Multifiber Reconstruction	51
	1 Introduction	51
	2 A Mixture of Wisharts Statistical Model	53
	3 Stable, Sparse, and Positive Deconvolution	57
	4 Experimental Results	60
	5 Conclusions	65
	Acknowledgments	65
	References	65
	The Algebra of Fourth-Order Tensors with Application to Diffusion MRI	69
	1 Introduction	69
	2 Second-Order Tensors	71
	3 Fourth-Order Tensors	74
	4 Symmetries of Fourth-Order Tensors	75
	5 Fourth-Order Tensors in 3D Space	77
	6 Material Symmetries	79
	7 Orientation Distributions and Orientation Tensors	84
	8 Fourth-Order Diffusion Tensors	89
	References	91
	Part II Higher-Level Analysis of Diffusion Images	93
	Structure-Specific Statistical Mapping of White Matter Tracts*	94
	1 Introduction	94
	2 Background	96
	3 Methods and Materials	97
	4 Experimental Evaluation	106
	5 Discussion and Conclusions	115
	Acknowledgements	119
	References	119
	Analysis of Distance/Similarity Measures for Diffusion Tensor Imaging	124
	1 Introduction	124
	2 Notation	125
	3 Properties	126
	4 Measures	128
	5 Methods	133
	6 Experiments	136
	7 Conclusions	144
	Acknowledgments	145
	References	145
	Part III Tensor Field Visualization	148
	Tensor Glyph Warping: Visualizing Metric Tensor Fields using Riemannian Exponential Maps	149
	1 Introduction	149
	2 Glyphs and Glyph Warping	150
	3 Related Work	151
	4 Tensors and Index Notation	155
	5 The Metric and Metric Spheres	157
	8 Solving the Geodesic Equation	161
	9 Geodesic Spheres and Warped Coordinate Systems	162
	10 The Logarithmic Map	162
	11 Experiments	164
	12 Conclusion	167
	Acknowledgments	168
	References	168
	Interactive Volume Rendering of Diffusion Tensor Data	171
	1 Introduction	171
	2 Volume Rendering	174
	3 Application and Results	178
	4 Conclusions and Future Work	183
	Acknowledgements	183
	References	184
	Dense Glyph Sampling for Visualization	187
	1 Introduction	187
	2 Related Work	188
	3 Assumptions and Goals	189
	4 Algorithm	190
	5 Structural Behavior	193
	6 Results	196
	7 Conclusion	200
	Acknowledgments	201
	References	201
	Part IV Tensor Field Analysis in the Physical Sciences	204
	The Role of Tensor Fields for Satellite Gravity Gradiometry	205
	1 Satellite Gravity Gradiometry	205
	2 Nonuniqueness Results	209
	3 Spherical Approach for SGG	210
	4 Decomposition of Spherical Tensor Fields	211