Rotational invariance based on Fourier analysis in polar and spherical coordinates

In this paper, polar and spherical Fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. The proposed transforms provide effective decompositions of an image into basic pat...

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Veröffentlicht in:IEEE transactions on pattern analysis and machine intelligence. - 1979. - 31(2009), 9 vom: 15. Sept., Seite 1715-22
1. Verfasser: Wang, Qing (VerfasserIn)
Weitere Verfasser: Ronneberger, Olaf, Burkhardt, Hans
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2009
Zugriff auf das übergeordnete Werk:IEEE transactions on pattern analysis and machine intelligence
Schlagworte:Journal Article Research Support, Non-U.S. Gov't
Beschreibung
Zusammenfassung:In this paper, polar and spherical Fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. The proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures. The theory is compactly presented with an emphasis on the analogy to the normal Fourier transform. The relation between the polar or spherical Fourier transform and the normal Fourier transform is explored. As examples of applications, rotation-invariant descriptors based on polar and spherical Fourier coefficients are tested on pattern classification problems
Beschreibung:Date Completed 06.10.2009
Date Revised 03.07.2009
published: Print
Citation Status MEDLINE
ISSN:1939-3539
DOI:10.1109/TPAMI.2009.29