The generalized totally geodesic Radon transform and its application to texture analysis

The generalized totally geodesic Radon transform associates the mean values over spherical tori to a function f defined on S3⊂H, where the elements of S3 are considered as quaternions representing rotations. It is introduced into the analysis of crystallographic preferred orientation and identified...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical methods in the applied sciences 2009-03, Vol.32 (4), p.379-394
Hauptverfasser: Bernstein, Swanhild, Hielscher, Ralf, Schaeben, Helmut
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The generalized totally geodesic Radon transform associates the mean values over spherical tori to a function f defined on S3⊂H, where the elements of S3 are considered as quaternions representing rotations. It is introduced into the analysis of crystallographic preferred orientation and identified with the probability density function corresponding to the angle distribution function W. Eventually, this communication suggests a new approach to recover an approximation of f from data sampling W. At the same time it provides additional clarification of a recently suggested method applying reproducing kernels and radial basis functions by instructive insight into its involved geometry. The focus is on the correspondence of geometrical and group features rather than on the mapping of functions and their spaces. Copyright © 2008 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.1042