Visualization and Processing of Tensor Fields: Advances and Perspectives (Mathematics and Visualization)

ThisbookattemptstocapturesomeoftheexcitementofaninspiringDagstuhl SeminarinJanuary2007. Theauthorsreportonrecentresearchresultsaswell as opining on future directions for the analysis and visualization of tensor ?elds. Topics range from applications of the analysis of tensor ?elds to purer researchintotheirmathematical andanalytical properties. Oneofthegoalsof thisseminarwastobringtogetherresearchersfromalongthatpure-to-applied disciplinary axis with the hope of fostering new collaborations and research. This book, we hope, will continue to further that goal in a broader context. Providence, Rhode Island, USA David H. Laidlaw Saarbruc ] ken, Saarland, Germany Joachim Weickert August 2008 Contents Part I Models for Di?usion MRI Modelling, Fitting and Sampling in Di?usion MRI Daniel C. Alexander. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Tensors, Polynomials and Models for Directional Data P. G. Batchelor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A Mixture of Wisharts (MOW) Model for Multi?ber Reconstruction ] Bing Jian, Baba C. Vemuri, and Evren Ozarslan. . . . . . . . . . . . . . . . . . . . . 39 The Algebra of Fourth-Order Tensors with Application to Di?usion MRI Maher Moakher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Part II Higher-Level Analysis of Di?usion Images Structure-Speci?c StatisticalMappingofWhiteMatterTracts Paul A. Yushkevich, Hui Zhang, Tony J. Simon, and James C. Gee. . . . 83 Analysis of Distance/Similarity Measures for Di?usion Tensor Imaging T. H. J. M. Peeters, P. R. Rodrigues, A. Vilanova, and B. M. ter Haar Romeny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 XContents Part III Tensor Field Visualization Tensor Glyph Warping: Visualizing Metric Tensor Fields using Riemannian Exponential Maps Anders Brun and Hans Knutsson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Interactive Volume Rendering of Di?usion Tensor Data Mario Hlawitschka, Gunther H. Weber, Alfred Anwander, Owen T. Carmichael, Bernd Hamann, and Gerik Scheuermann. . . . . . . . 161 Dense Glyph Sampling for Visualization Louis Feng, Ingrid Hotz, Bernd Hamann, and Kenneth Joy. . . . . . . . . . . .

Matrix-valued data sets - so-called second order tensor fields -
have gained significant importance in scientific visualization and
image processing due to recent developments such as diffusion tensor
imaging. This book is the first edited volume that presents the
state-of-the-art in the visualization and processing of tensor fields.
It contains some longer chapters dedicated to surveys and tutorials of
specific topics, as well as a great deal of original work by leading
experts that has not been published before. It serves as an overview
for the inquiring scientist, as a basic foundation for developers and
practitioners, and as as a textbook for specialized classes and seminars
for graduate and doctoral students.