Rotational invariance based on Fourier analysis in polar and spherical coordinates.

Full 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 problems.

Author information

Author/s: Wang, Qing (Q); Ronneberger, Olaf (O); Burkhardt, Hans (H);

Affiliation: Computer Science Department and the Centre for Biological Signaling Studies, University of Freiburg, Freiburg, Germany. qwang(-atsign-)informatik.uni-freiburg.de

Journal and publication information

Publication Type: Journal Article; Research Support, Non-U.S. Gov't

Journal: IEEE transactions on pattern analysis and machine intelligence (IEEE Trans Pattern Anal Mach Intell), published in United States. (Language: eng)

Reference: 2009-Sep; vol 31 (issue 9) : pp 1715-22

Dates: Created 2009/07/03; Completed 2009/10/06;

PMID: 19574630, status: MEDLINE (last retrieval date: 10/6/2009, IMS Date: )

Sourced from the National Library of Medicine. Abstract text and other information may be subject to copyright.

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