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. . . . . . . . . . . .