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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 arount 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.
List of contents
Models for Diffusion MRI.- Modelling, Fitting and Sampling in Diffusion MRI.- Tensors, Polynomials and Models for Directional Data.- A Mixture of Wisharts (MOW) Model for Multifiber Reconstruction.- The Algebra of Fourth-Order Tensors with Application to Diffusion MRI.- Higher-Level Analysis of Diffusion Images.- Structure-Specific Statistical Mapping of White Matter Tracts.- Analysis of Distance/Similarity Measures for Diffusion Tensor Imaging.- Tensor Field Visualization.- Tensor Glyph Warping: Visualizing Metric Tensor Fields using Riemannian Exponential Maps.- Interactive Volume Rendering of Diffusion Tensor Data.- Dense Glyph Sampling for Visualization.- Tensor Field Analysis in the Physical Sciences.- The Role of Tensor Fields for Satellite Gravity Gradiometry.- Tensor Visualization and Defect Detection for Nematic Liquid Crystals using Shape Characteristics.- A Tensor Approach to Elastography Analysis and Visualization.- Tensor Image Structure Models.- A Higher-Order Structure Tensor.- Monogenic Curvature Tensor as Image Model.- Filtering with Tensors.- A General Structure Tensor Concept and Coherence-Enhancing Diffusion Filtering for Matrix Fields.- Coordinates-Based Diffusion Over the Space of Symmetric Positive-Definite Matrices.- Variational Methods for Denoising Matrix Fields.- An Operator Algebraic Inverse Scale Space Method for Symmetric Matrix Valued Images.
About the author
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.
Summary
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.
