Titlebook: Visualization and Processing of Tensor Fields; Advances and Perspec David Laidlaw,Joachim Weickert Book 2009 Springer-Verlag Berlin Heidelb

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The Algebra of Fourth-Order Tensors with Application to Diffusion MRIr tensor in three-dimensional space by a second-order tensor in a six-dimensional space. Such a representation makes the manipulation of fourth-order tensors similar to that of the more familiar second-order tensors. We discuss the algebra of the space of fourth-order symmetric tensors and describe

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Tensor Glyph Warping: Visualizing Metric Tensor Fields using Riemannian Exponential Mapsderive the well-known metric sphere glyph from the geodesic equation, where the tensor field to be visualized is regarded as the metric of a manifold. These glyphs capture the appearance of the tensors relative to the coordinate system of the human observer. We then introduce two new concepts for me

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Interactive Volume Rendering of Diffusion Tensor Dataedical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of

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Dense Glyph Sampling for Visualizationsamples are useful for many visualization and graphics applications. The glyphs are embedded in a set of nonoverlapping ellipses whose size and density match a given anisotropic metric. An additional parameter controls the arrangement of the ellipses on lines, which can be favorable for some applica

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The Role of Tensor Fields for Satellite Gravity Gradiometryy a gradiometer are – for a so-called full gradiometer – all second-order derivatives of the potential, that is, the Hessian tensor. This leads to a nonstandard problem in potential theory..After a short description of satellite gradiometry, we focus on uniqueness and existence problems. For this, a

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A Tensor Approach to Elastography Analysis and Visualizationr of tissues can be analyzed with tensor signal processing. In this work, we propose an analysis of elastography through the deformation tensor and its decomposition into both strain and vorticity tensors. The vorticity gives information about the rotation of the inclusions (simulated tumors) that m

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A Higher-Order Structure Tensor second-order model to a higher-order structure tensor (HOST), which is able to model more than one significant orientation, as found in corners, junctions, and multichannel images. We provide a theoretical analysis and a number of mathematical tools that facilitate practical use of the HOST, visual