The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion (2009)
R. Hielscher, D. Potts, J. Prestin, H. Schaeben, M. Schmalz
The inversion of the one–dimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem which applies to X–ray tomography with polycrystalline materials. This...
The Radon Transform on SO(3):A Fourier Slice Theorem and (2008)
Numerical Inversion, R. Hielscher, D. Potts, J. Prestin, H. Schaeben, M. Schmalz
The inversion of the one-dimensional Radon transform on the rotation groupSO (3) is an ill posed inverse problem which applies to X-ray tomography withpolycrystalline materials. This communication...
Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals (2008)
Egozcue, J.J. (Juan José), Mackenzie, J.R., Heilbronner, R., Hielscher, R., Müller, A., Schaeben, H.
A novel test of spatial independence of the distribution of crystals or phases in rocksbased on compositional statistics is introduced. It improves and generalizes the commonjoins-count statistics...
The Generalized Spherical Radon Transform and Its Application in Texture Analysis (2005)
Bernstein, S., Hielscher, R., Schaeben, H.
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are...
Tracer Test in the Bowden Close Passive Treatment System (UK) – Preliminary Results (2005)
B. Merkel, H. Schaeben, Ch. Wolkersdorfer, A Hasche (hrsg, Wissenschaftliche Mitteilungen, ...
A mine water tracer test with bromide, Na-fluorescein, and NaCl was conducted at the Bowden Close passive treatment system in County Durham, UK. This passive treatment system comprises two RAPS units...
The de la Vallée Poussin Standard Orientation Density Function (1999)
The de la Vallée Poussin standard orientation density function νκ(ω)=C(κ)cos2κ(ω/2) is discussed with emphasis on the finiteness of its harmonic series expansion which, advantageously...
A Brief Survey of Spherical Interpolation and Approximation Methods for Texture Analysis (1996)
In texture analysis there are several instances when mathematical methods of spherical interpolation or approximation are required. Ad hoc adaptions of univariate or bivariate methods to the topology...
A Unified View of Methods to Resolve the Inverse Problem of Texture Goniometry (1996)
Invariants of the tomographic projection operator of texture goniometry and counterexamples provide a unified view of existing methods to resolve the corresponding inverse problem and may be...
A Note on a Generalized Standard Orientation Distribution in PDF-Component Fit Methods (1995)
A generalized model orientation distribution which was recently introduced into texture analysis is identified as von Mises-Fisher matrix distribution on SO(3) or, equivalently, as Bingham...
Numerical Determination of the Variation Width of Feasible ODFs (1993)
Within all known methods of calculating a model orientation density (odf) from a given set of pole densities (pdfs) the set of all feasible odfs and in particular its associated variation width...
“Normal” Orientation Distributions (1992)
Analogues of the normal distribution in Euclidean space for orientations represented by Rodrigues parameters are discussed. It is emphasized that different characterizations of the normal...
Parameterizations and Probability Distributions of Orientations (1990)
General normal distributions of orientations (proper rotations) with respect to different parameterizations are mathematically rigorously and notationally concisely represented. This includes their...
Normalizing Incomplete Experimental Pole Figures by Means of the Vector Method (1984)
The vector method of quantitative texture analysis provides a new solution of the problem of normalizing incomplete experimental pole figures. It basically makes use of the fact that the matrix...
Introducing a Conditional Ghost Correction Into the Vector Method (1984)
The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of...