Discrete tomographic reconstruction of 2D polycrystal orientation maps from X-ray diffraction projections using Gibbs priors

L. Rodek; E. Knudsen; H.F. Poulsen; G.T. Herman

doi:10.1016/j.endm.2005.05.077

Discrete tomographic reconstruction of 2D polycrystal orientation maps from X-ray diffraction projections using Gibbs priors

L. Rodek
, E. Knudsen
, H.F. Poulsen
, G.T. Herman

Research output: Contribution to journal › Conference article › Research

Abstract

The determination of crystalline structures is a demanding and fundamental task of crystallography. This paper offers a new approach for rendering a 2D grain map of a polycrystal based on an orientation map reconstructed from X-ray diffraction patterns. The orientation map is produced by a Bayesian discrete tomographic algorithm, applying image-modelling Gibbs priors and a homogeneity condition. The optimization of the objective function is accomplished via the Gibbs Sampler in conjunction with simulated annealing. In order to express the structure of the orientation map, the similarity of orientations is defined by means of quaternions.

Original language	English
Journal	Electronic Notes in Discrete Mathematics
Volume	20
Pages (from-to)	439-453
ISSN	1571-0653
DOIs	https://doi.org/10.1016/j.endm.2005.05.077
Publication status	Published - 1 Jul 2005
Event	Workshop on Discrete Tomography and its Applications - City University of New York, New York, United States Duration: 13 Jun 2005 → 15 Jun 2005

Workshop

Workshop	Workshop on Discrete Tomography and its Applications
Location	City University of New York
Country/Territory	United States
City	New York
Period	13/06/2005 → 15/06/2005

Keywords

discrete tomography
simulated annealing
optimization
crystallography
polycrystal
orientation map
X-ray diffraction
quaternion

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10.1016/j.endm.2005.05.077

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@inproceedings{7617e51c4ee34f98bdf26b7e16019ac1,

title = "Discrete tomographic reconstruction of 2D polycrystal orientation maps from X-ray diffraction projections using Gibbs priors",

abstract = "The determination of crystalline structures is a demanding and fundamental task of crystallography. This paper offers a new approach for rendering a 2D grain map of a polycrystal based on an orientation map reconstructed from X-ray diffraction patterns. The orientation map is produced by a Bayesian discrete tomographic algorithm, applying image-modelling Gibbs priors and a homogeneity condition. The optimization of the objective function is accomplished via the Gibbs Sampler in conjunction with simulated annealing. In order to express the structure of the orientation map, the similarity of orientations is defined by means of quaternions.",

keywords = "7-I poly, discrete tomography, simulated annealing, optimization, crystallography, polycrystal, orientation map, X-ray diffraction, quaternion",

author = "L. Rodek and E. Knudsen and H.F. Poulsen and G.T. Herman",

year = "2005",

month = jul,

day = "1",

doi = "10.1016/j.endm.2005.05.077",

language = "English",

volume = "20",

pages = "439--453",

journal = "Electronic Notes in Discrete Mathematics",

issn = "1571-0653",

publisher = "Elsevier",

note = "Workshop on Discrete Tomography and its Applications ; Conference date: 13-06-2005 Through 15-06-2005",

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TY - GEN

T1 - Discrete tomographic reconstruction of 2D polycrystal orientation maps from X-ray diffraction projections using Gibbs priors

AU - Rodek, L.

AU - Knudsen, E.

AU - Poulsen, H.F.

AU - Herman, G.T.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - The determination of crystalline structures is a demanding and fundamental task of crystallography. This paper offers a new approach for rendering a 2D grain map of a polycrystal based on an orientation map reconstructed from X-ray diffraction patterns. The orientation map is produced by a Bayesian discrete tomographic algorithm, applying image-modelling Gibbs priors and a homogeneity condition. The optimization of the objective function is accomplished via the Gibbs Sampler in conjunction with simulated annealing. In order to express the structure of the orientation map, the similarity of orientations is defined by means of quaternions.

AB - The determination of crystalline structures is a demanding and fundamental task of crystallography. This paper offers a new approach for rendering a 2D grain map of a polycrystal based on an orientation map reconstructed from X-ray diffraction patterns. The orientation map is produced by a Bayesian discrete tomographic algorithm, applying image-modelling Gibbs priors and a homogeneity condition. The optimization of the objective function is accomplished via the Gibbs Sampler in conjunction with simulated annealing. In order to express the structure of the orientation map, the similarity of orientations is defined by means of quaternions.

KW - 7-I poly

KW - discrete tomography

KW - simulated annealing

KW - optimization

KW - crystallography

KW - polycrystal

KW - orientation map

KW - X-ray diffraction

KW - quaternion

U2 - 10.1016/j.endm.2005.05.077

DO - 10.1016/j.endm.2005.05.077

M3 - Conference article

SN - 1571-0653

VL - 20

SP - 439

EP - 453

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

T2 - Workshop on Discrete Tomography and its Applications

Y2 - 13 June 2005 through 15 June 2005

ER -

Discrete tomographic reconstruction of 2D polycrystal orientation maps from X-ray diffraction projections using Gibbs priors

Abstract

Workshop

Keywords

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