Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 26, Issue 1-2, Pages 5-18Publisher
SPRINGER
DOI: 10.1007/s10851-006-3605-y
Keywords
multi-dimensional Fourier transform; Clifford analysis
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Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced, including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued kernel. In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained, leading to further properties, both in the L-1 and in the L-2 context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced.
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