Synopses & Reviews
Visualisation and Processing of Tensor Fields provides researchers an inspirational look at how to process and visualize complicated 2D and 3D images known as tensor fields. Tensor fields are the natural representation for many physical quantities; they can describe how water moves around in the brain, how gravity varies around the earth, or how materials are stressed and deformed. With its numerous color figures, this book helps the reader understand both the underlying mathematics and the applications of tensor fields. The reader also will learn about the most recent research topics and open research questions.
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.
Table of Contents
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 Tensor Concept 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