The exact vacuum polarization 4-tensor in the presence of a static magnetic field is calculated by a method due to Svetozarova and Tsytovich. The Hermitian part of the tensor is explicitly renormalized by Shabad’s diagonalization with respect to tensor indices and the anti-Hermitian part of the tensor is found to be finite and gauge invariant. An alternative method for calculating the vacuum po...

The regularized iterative reconstruction of the tensor field in diffusion tensor tomography magnetic resonance imaging was investigated. The total variation constraints on eigenvalue and tensor component images of the diffusion tensor were explored. A computer generated phantom was used to simulate the diffusion tensor in a cardiac MRI study in which the diffusion model depended upon the fiber ...

We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold.We also investigate some properties of curvature tensor, conformal curvature tensor,W2curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor...

Tensor valued data are frequently used in medical imaging. For a 3-dimensional second order tensor such data imply at least six degrees of freedom for each voxel. The operators ability to perceive this information is of outmost importance and in many cases a limiting factor for the interpretation of the data. In this paper we propose a decomposition of such tensor fields using the Tflash tensor...

Recently, diffusion tensor imaging is attracting the biomedical researchers for its application in depiction of fiber tracts based on diffusion anisotropy. In this paper, we briefly describe the basic theory of diffusion tensor MR imaging, the determination process of diffusion tensor, and the basic concepts of diffusion tensor visualization techniques. Several results of clinical application i...

We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N -way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and “matricization.” We have further added two classes for representing tensors in decomposed format: cp tensor and tucker tensor. We demonstrate the use o...

In this paper, we deal with the problem of spherical interpolation of discretely given data of tensorial type. To this end, spherical tensor elds are investigated and a decomposition formula is described. It is pointed out that the decomposition formula is of importance for the spectral analysis of the gra-vitational tensor in (spaceborne) gradiometry. Tensor spherical harmonics are introduced ...

Many image processing methods such as corner detection, optical flow and iterative enhancement make use of image tensors. Generally, these tensors are estimated using the structure tensor. In this work we show that the gradient energy tensor can be used as an alternative to the structure tensor in several cases. We apply the gradient energy tensor to common image problem applications such as co...

The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel-Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton’s tensor (i) is completely symmetric, and (ii) has a trace-free divergence if Einstein-Maxwell equations hold. It follows that the trac...

In this chapter we define the topology of 2D asymmetric tensor fields in terms of two graphs corresponding to the eigenvalue and eigenvector analysis for the tensor fields, respectively. Asymmetric tensor field topology can not only yield a concise representation of the field, but also provide a framework for spatial-temporal tracking of field features. Furthermore, inherent topological constra...