Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (eBook)

Part I: Mathematical Foundations: 1 Cem Yolcu and Evren Özarslan: Diffusion-Weighted Magnetic Resonance Signal for General Gradient Waveforms: Multiple Correlation Function Framework, Path Integrals, and Parallels Between Them.- 2 T.C.J. Dela Haije, A. Fuster and L.M.J. Florack: Finslerian Diffusion and the Bloch-Torrey Equation.- 3 M. Moakher and P. J. Basser: Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries.- 4 Yue Zhang, Jonathan Palacios and Eugene Zhang: Topology of 3D Linear Symmetric Tensor Fields.- 5 Carmeliza Navasca and Deonnia N. Pompey: Random Projections for Low Multilinear Rank Tensors.- Part II: Processing, Filtering and Interpolation: 6 Jasper J. van de Gronde, Mikola Lysenko and Jos B.T.M. Roerdink: Path-Based Mathematical Morphology on Tensor Fields.- 7 Andreas Kleefeld and Bernhard Burgeth: Processing Multispectral Images via Mathematical Morphology.- 8 Luc Florack, Tom Dela Haije and Andrea Fuster: Direction-Controlled DTI Interpolation.- 9 Daniel Jörgens and Rodrigo Moreno: Tensor Voting: Current State, Challenges and New Trends in the Context of Medical Image Analysis.- Part III: Visualization: 10 Olivier Vaillancourt, Maxime Chamberland, Jean-Christophe Houde and Maxime Descoteaux: Visualization of Diffusion Propagator and Multiple Parameter Diffusion Signal.- 11 Sujal Bista, Jiachen Zhuo, Rao P. Gullapalli and Amitabh Varshney: Visual Knowledge Discovery for Diffusion Kurtosis Datasets of the Human Brain.- 12 Tobias Isenberg: A Survey of Illustrative Visualization Techniques for Diffusion-Weighted MRI Tractography.- 13 Valentin Zobel, Jan Reininghaus and Ingrid Hotz: Visualizing Symmetric Indefinite 2D Tensor Fields  Using the Heat Kernel Signature.- Part IV: Statistical Analysis: 14 Maxime Taquet, Benoit Scherrer and Simon K. Warfield: A Framework for the Analysis of Diffusion Compartment Imaging (DCT).- 15 Lauren J. O’Donnell and Thomas Schultz: Statistical and Machine Learning Methods for Neuroimaging: Examples, Challenges, and Extensions to Diffusion Imaging Data.- Part V: Applications: 16 A. Maries, T. Luciani, P.H. Pisciuneri, M.B. Nik, S.L. Yilmaz, P. Givi and G.E.  Marai : A Clustering Method for Identifying Regions of Interest in Turbulent Combustion Tensor Fields.- 17 Mark Schöneich, Andrea Kratz, Valentin Zobel, Gerik Scheuermann, Markus Stommel, and Ingrid Hotz: Tensor Lines in Engineering – Success, Failure, and Open Questions.- 18 Vesna Prchkovska, Magí Andorrà , Pablo Villoslada, Eloy Martinez-Heras, Remco Duits, David Fortin, Paulo Rodrigues and Maxime Descoteaux: Contextual Diffusion Image Post-Processing Aids Clinical Applications.