We introduce a framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation makes it possible to define...

This paper proposes the Mesh Neural Network (MNN), a novel architecture which allows neurons to be connected in any topology, efficiently route information. In MNNs, information is propagated between throughout state transition function. State and error gradients are then directly computed from updates without backward computation. The MNN propagation schema formalized derived tensor algebra. p...

We introduce a mathematical framework for computing geometrical properties of white matter fibers directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it ...

This paper describes a technique for characterization and segmentation of anisotropic patterns that exhibit a single local orientation. Using Gaussian derivatives we construct a gradient-square tensor at a selected scale. Smoothing of this tensor allows us to combine information in a local neighborhood without canceling vectors pointing in opposite directions. Whereas opposite vectors would can...

The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. Similarly in electro-magnetic theory Maxwell’s equations can be written as first order differential equations in the field tensor Fab and this in can be ...

In this paper we present new insights in methods to solve the orientation representation problem in arbitrary dimensions. The gradient structure tensor is one of the most used descriptors for local structure in multi-dimensional images. We will relate its properties to the double angle method (2D) and the Knutsson mapping. We present a general scheme to reduce the dimensionality of the mappings...

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams...

An important problem in medical image analysis is the segmentation of anatomical regions of interest. Once regions of interest are segmented, one can extract shape, appearance, and structural features that can be analyzed for disease diagnosis or treatment evaluation. Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new medical imaging modality that captures unique water dif...