Visualization and Processing of Tensor Fields: Advances and Perspectives

ISBN-13: 9783642100031 / Angielski / Miękka / 2010 / 376 str.

David H. Laidlaw; Joachim Weickert

Opis

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. . . . . . . . . . . ."

Spis treści

Part I MODELS FOR DIFFUSION MRI Modelling, Fitting and Sampling in Diffusion MRI - Daniel C Alexander Tensors, Polynomials, and Models for Directional Data - P. G. Batchelor A Mixture of Wisharts (MOW) Model for Multi-fiber Reconstruction - Bing Jian, Baba C. Vemuri, Evren ¨Ozarslan The Algebra of Fourth-Order Tensors with Application to Diffusion MRI - Maher Moakher Part II HIGHER-LEVEL ANALYSIS OF DIFFUSION IMAGES Structure-Specific Statistical Mapping of White Matter Tracts - Paul A. Yushkevich, Hui Zhang, Tony J. Simon, James C. Gee Analysis of distance/similarity measures for Diffusion Tensor Imaging - T.H.J.M. Peeters, P.R. Rodrigues, A. Vilanova, B.M. ter Haar Romeny Part III TENSOR FIELD VISUALIZATION Tensor Glyph Warping – Visualizing Metric Tensor Fields using Riemannian Exponential Maps - Anders Brun, Hans Knutsson Interactive Volume Rendering of Diffusion Tensor Data - Mario Hlawitschka, Gunther H. Weber, Alfred Anwander, Owen T. Carmichael, Bernd Hamann, Gerik Scheuermann Dense Glyph Sampling for Visualization - Louis Feng, Ingrid Hotz, Bernd Hamann, Kenneth Joy Part IV TENSOR FIELD ANALYSIS IN THE PHYSICAL SCIENCES The Role of Tensor Fields for Satellite Gravity Gradiometry - Michael Schreiner Tensor Visualization and Defect Detection for Nematic Liquid Crystals using Shape Characteristics - T.J. Jankun-Kelly, Song Zhang, A. C. Callan-Jones, Robert A. Pelcovits, V. A. Slavin, David H. Laidlaw A Tensor Approach to Elastography Analysis and Visualization - D. Sosa-Cabrera1, M.A. Rodriguez-Florido, E. Suarez-Santana and Juan Ruiz-Alzola Part V TENSOR IMAGE STRUCTURE MODELS A Higher-Order Structure Tensor - Thomas Schultz, Joachim Weickert, Hans-Peter Seidel Monogenic Curvature Tensor as Image Model - Gerald Sommer, Lennart Wietzke and Di Zang Part VI FILTERING WITH TENSORS A General Structure TensorConcept and Coherence-Enhancing Diffusion Filtering for Matrix Fields - Bernhard Burgeth, Stephan Didas, Joachim Weickert Coordinates-based diffusion over the space of symmetric positive-definite matrices - Yaniv Gur and Nir Sochen Variational methods for denoising matrix fields - S. Setzer, G. Steidl, B. Popilka, B. Burgeth An Operator Algebraic Inverse Scale Space Method for Symmetric Matrix Valued Images - Johan Lie, Bernhard Burgeth, Oddvar Christiansen

O autorze

Joachim Weickert is Full Professor of Mathematics and Computer Science at Saarland University (Saarbrücken, Germany) where he heads the Mathematical Image Analysis Group. He performs research in image processing, computer vision and scientific computing, focusing on techniques based on partial differential equations and variational methods.