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...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2009-03, Vol.32 (4), p.379-394 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Bernstein, Swanhild Hielscher, Ralf Schaeben, Helmut |
| description | 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. |
| doi_str_mv | 10.1002/mma.1042 |
| format | Article |
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Copyright © 2008 John Wiley & Sons, Ltd.</description><subject>Abstract harmonic analysis</subject><subject>crystallography</subject><subject>Differential geometry</subject><subject>Exact sciences and technology</subject><subject>Functional analysis</subject><subject>Geometry</subject><subject>Global analysis, analysis on manifolds</subject><subject>harmonic analysis</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Sciences and techniques of general use</subject><subject>texture analysis</subject><subject>Topology. Manifolds and cell complexes. 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| ispartof | Mathematical methods in the applied sciences, 2009-03, Vol.32 (4), p.379-394 |
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| language | eng |
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| source | Wiley Online Library - AutoHoldings Journals |
| subjects | Abstract harmonic analysis crystallography Differential geometry Exact sciences and technology Functional analysis Geometry Global analysis, analysis on manifolds harmonic analysis Mathematical analysis Mathematics Sciences and techniques of general use texture analysis Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds totally geodesic Radon transform |
| title | The generalized totally geodesic Radon transform and its application to texture analysis |
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