Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates

Summary: Rotational Invariance Based on Fourier
Analysis in Polar and Spherical Coordinates
Qing Wang, Olaf Ronneberger, and
Hans Burkhardt, Member, IEEE
Abstract--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
Index Terms--Invariants, Fourier analysis, radial transform, multidimensional.
NOTHING needs to be said about the importance of Fourier
transform in image processing and pattern recognition. Usually,
Fourier transform is formulated in Cartesian coordinates, where a


Source: Albert-Ludwigs-Universität Freiburg, Institut für Informatik,, Lehrstuhls für Mustererkennung und Bildverarbeitung


Collections: Computer Technologies and Information Sciences