Locally Anisotropic Gravity and Strings

An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of Kaluza--Klein and/or extensions of Lagrange and Finsler spaces) is presented. The conditions for consistent propagation of closed strings in locally anisotropic background spaces are analyzed. The connection between the conformal invariance, the vanishing of the renormalization group beta--function of the generalized sigma--model and field equations of locally anisotropic gravity is studied in detail.Comment: 49 pages, Revtex, a short variant is submitted to Nucl. Phys.

Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI

In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset having 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization technique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares filter directly incorporated in the tracing algorithm

Quantitative Susceptibility Mapping: Contrast Mechanisms and Clinical Applications.

Quantitative susceptibility mapping (QSM) is a recently developed MRI technique for quantifying the spatial distribution of magnetic susceptibility within biological tissues. It first uses the frequency shift in the MRI signal to map the magnetic field profile within the tissue. The resulting field map is then used to determine the spatial distribution of the underlying magnetic susceptibility by solving an inverse problem. The solution is achieved by deconvolving the field map with a dipole field, under the assumption that the magnetic field is a result of the superposition of the dipole fields generated by all voxels and that each voxel has its unique magnetic susceptibility. QSM provides improved contrast to noise ratio for certain tissues and structures compared to its magnitude counterpart. More importantly, magnetic susceptibility is a direct reflection of the molecular composition and cellular architecture of the tissue. Consequently, by quantifying magnetic susceptibility, QSM is becoming a quantitative imaging approach for characterizing normal and pathological tissue properties. This article reviews the mechanism generating susceptibility contrast within tissues and some associated applications

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation