Fourier transform magnitudes are unique pattern recognition templates

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in...

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Bibliographic Details
Published inBiological cybernetics Vol. 54; no. 6; p. 385
Main Authors Gardenier, P H, McCallum, B C, Bates, R H
Format Journal Article
LanguageEnglish
Published Germany 01.01.1986
Subjects
Fourier Analysis
Humans
Mathematics
Models, Biological
Pattern Recognition, Automated
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Summary:Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.
ISSN:0340-1200
DOI:10.1007/BF00355544