A method has been developed to determine orientation distribution function (ODF) of anisotropic paramagnetic species by analysis of the angular dependence of the ESR spectra. The method is based on computational spectra simulation. The ODF is represented as an expansion in terms of orthonormal functions. The expansion coefficients are determined through minimization of discrepancies between sim...

A technique to quantify the uncertainty in an estimated orientation distribution function (ODF) by propagating the uncertainty from measured pole figures is demonstrated in this paper using Monte Carlo techniques and the Matlab toolbox for quantitative texture analysis. Unlike the uncertainty in the measured pole figures, where small values of intensity correlate to high uncertainty, uncertaint...

A software package for the calculation of diffraction elastic constants (DEC) for materials both with and without preferred orientation was developed. All grain-interaction models that can use the crystallite orientation distribution function (ODF) are incorporated, including Kröner, Hill, inverse Kröner, and Reuss. The functions of the software include: reading the ODF in common textual format...

The task of reconstruction of microstructures from their limited description is posed as a maximum entropy (MaxEnt) problem. Microstructural descriptors are taken in the form of volume fractions, correlation functions and grain sizes. Morphological and size quantifications are used as features of microstructure and samples consistent with these features are reconstructed. The nonuniqueness of t...

Introduction. The geometric median is a classic robust estimator of centrality for data in Euclidean spaces, and it has been generalized in analytical manifold in [1]. Recently, an intrinsic Riemannian framework for Orientation Distribution Function (ODF) was proposed for the calculation in ODF field [2]. In this work, we prove the unique existence of the Riemannian median in ODF space. Then we...

High angular resolution diffusion imaging (HARDI) has become an important magnetic resonance technique for in vivo imaging. Current techniques for estimating the diffusion orientation distribution function (ODF), i.e., the probability density function of water diffusion along any direction, do not enforce the estimated ODF to be nonnegative or to sum up to one. Very often this leads to an estim...

Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed...

By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order rea...

By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order rea...

Current methods in high angular resolution diffusion imaging (HARDI) estimate the probability density function of water diffusion as a continuous-valued orientation distribution function (ODF) on the sphere. However, such methods could produce an ODF with negative values, because they enforce non-negativity only at finitely many directions. In this paper, we propose to enforce non-negativity on...