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

Endemic

An Operator Algebraic Inverse Scale Space Method for Symmetric Matrix Valued Imagesng of Matrix Fields with Singular PDEs. In .. Volume 4485 of ., pages 556–567. Springer, Heidelberg, 2007). We perform numerical experiments on synthetic tensor fields and on real diffusion tensor data from DT-MRI of a human brain.

著名

The Role of Tensor Fields for Satellite Gravity Gradiometry certain decomposition of the Hessian tensor is of importance. The decomposition allows in addition to transfer modern solution methods for scalar functions on the sphere to the tensorial case, by generalizing zonal functions to zonal tensor kernels.

混雜人

The Algebra of Fourth-Order Tensors with Application to Diffusion MRItensors similar to that of the more familiar second-order tensors. We discuss the algebra of the space of fourth-order symmetric tensors and describe different metrics on this space. Special emphasis is placed on totally symmetric tensors and on orientation tensors. Applications to high angular resolution diffusion imaging are discussed.

MENT

碎片

Structure-Specific Statistical Mapping of White Matter Tractsnd accounting for errors in normalization. The framework enables the analysis of individual white matter structures, and provides a range of possibilities for computing statistics and visualizing differences between cohorts. The framework is demonstrated in a study of white matter differences in pediatric chromosome 22q11.2 deletion syndrome.

責(zé)問

THROB

Tensors, Polynomials and Models for Directional Data to compare models, as one of the tensor representations is polynomial. Thus a multivariate Taylor expansion uses Higher Order Tensors, and models will use an expansion in higher order polynomials. We show provide formulas for different model-to-model conversions.

輕浮思想

Tensor Visualization and Defect Detection for Nematic Liquid Crystals using Shape Characteristicszation. One set of characteristics are based on the physics of the liquid crystal system (a real, symmetric, traceless tensor); the other set is an application of the well known Westin DT-MRI shape characteristics. These shape metrics are used both for direct tensor visualization and for detection of defects within the liquid crystal matrix.

情感脆弱

Monogenic Curvature Tensor as Image Models. By combining differential geometry and Clifford analysis, the monogenic curvature tensor can be derived to perform a split of identity and to enable simultaneous estimation of local amplitude, phase, main orientation, and angle of intersection in a monogenic scale-space framework.

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978-3-642-10003-1Springer-Verlag Berlin Heidelberg 2009