Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids

H. Schaeben; R. Hielscher; J. J. Fundenberger; D. Potts; J. Prestin

Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids

H. Schaeben, R. Hielscher, J. J. Fundenberger, D. Potts, J. Prestin

Institute of Mathematics

Abstract

Due to a novel method of pole intensity to orientation density inversion applying radial basis functions and an implementation employing fast Fourier transform algorithms for S² , S²× S², and SO(3) it is now possible to process intensity data arbitrarily scattered on the pole sphere and successively compute numerical approximations of an ODF explaining the data while they are being measured. Therefore we suggest an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. At each level of refinement an ODF is computed, and the refinement is terminated if some stopping rule is accomplished.

Original language	English
Pages	48-50
Number of pages	3
Publication status	Published - 01.01.2007
Event	Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007 - Beijing, China Duration: 26.08.2007 → 31.08.2007 Conference number: 105720

Conference

Conference	Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007
Abbreviated title	IAMG 2007
Country/Territory	China
City	Beijing
Period	26.08.07 → 31.08.07

Cite this

Schaeben, H., Hielscher, R., Fundenberger, J. J., Potts, D., & Prestin, J. (2007). Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids. 48-50. Paper presented at Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007
, Beijing, China.

Schaeben, H. ; Hielscher, R. ; Fundenberger, J. J. et al. / Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids. Paper presented at Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007
, Beijing, China.3 p.

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title = "Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids",

abstract = "Due to a novel method of pole intensity to orientation density inversion applying radial basis functions and an implementation employing fast Fourier transform algorithms for S2 , S2× S2, and SO(3) it is now possible to process intensity data arbitrarily scattered on the pole sphere and successively compute numerical approximations of an ODF explaining the data while they are being measured. Therefore we suggest an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. At each level of refinement an ODF is computed, and the refinement is terminated if some stopping rule is accomplished.",

author = "H. Schaeben and R. Hielscher and Fundenberger, {J. J.} and D. Potts and J. Prestin",

year = "2007",

month = jan,

day = "1",

language = "English",

pages = "48--50",

note = "Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007<br/>, IAMG 2007 ; Conference date: 26-08-2007 Through 31-08-2007",

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Schaeben, H, Hielscher, R, Fundenberger, JJ, Potts, D & Prestin, J 2007, 'Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids', Paper presented at Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007
, Beijing, China, 26.08.07 - 31.08.07 pp. 48-50.

Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids. / Schaeben, H.; Hielscher, R.; Fundenberger, J. J. et al.
2007. 48-50 Paper presented at Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007
, Beijing, China.

Research output: Contribution to conference › Conference Papers › peer-review

TY - CONF

T1 - Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids

AU - Schaeben, H.

AU - Hielscher, R.

AU - Fundenberger, J. J.

AU - Potts, D.

AU - Prestin, J.

N1 - Conference code: 105720

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Due to a novel method of pole intensity to orientation density inversion applying radial basis functions and an implementation employing fast Fourier transform algorithms for S2 , S2× S2, and SO(3) it is now possible to process intensity data arbitrarily scattered on the pole sphere and successively compute numerical approximations of an ODF explaining the data while they are being measured. Therefore we suggest an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. At each level of refinement an ODF is computed, and the refinement is terminated if some stopping rule is accomplished.

AB - Due to a novel method of pole intensity to orientation density inversion applying radial basis functions and an implementation employing fast Fourier transform algorithms for S2 , S2× S2, and SO(3) it is now possible to process intensity data arbitrarily scattered on the pole sphere and successively compute numerical approximations of an ODF explaining the data while they are being measured. Therefore we suggest an adaptive successive refinement of an initial coarse uniform grid to a locally refined grid where the progressive refinement corresponds to the pattern of preferred crystallographic orientation. At each level of refinement an ODF is computed, and the refinement is terminated if some stopping rule is accomplished.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-84902602230&origin=inward&txGid=9bd435e75f65a00f9a4ccf80fb564760

M3 - Conference Papers

SP - 48

EP - 50

T2 - Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007<br/>

Y2 - 26 August 2007 through 31 August 2007

ER -

Schaeben H, Hielscher R, Fundenberger JJ, Potts D, Prestin J. Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids. 2007. Paper presented at Annual Conference of the International Association for Mathematical Geology: Geomathematics and GIS Analysis of Resources, Environment and Hazards 2007
, Beijing, China.

Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids

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Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids

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High resolution texture analysis

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