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Lookup NU author(s): Professor Said Boussakta
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Three-dimensional convolutions and correlations are used for three-dimensional image-processing applications. Their calculation involves extensive computation, which makes the use of fast transforms very advantageous. As the number of arithmetic operations is very large, the accumulation of rounding or truncation errors arising in the use of the fast Fourier and Hartley transforms tends to increase. Number theoretic transforms are calculated module an integer and hence they are not subject to these errors. Recently a one-dimensional transform called the new Mersenne number transform (NMNT) was introduced and applied successfully to the calculation of 1-D convolutions/correlations. Unlike other Mersenne number transforms, the NMNT can handle long data sequences and has fast algorithms. In the paper, the 1-D definitions are first extended to the 3-D case in detail for use in 3-D image processing applications. The concept and derivation of the 3-D vector radix algorithm is then introduced for the fast calculation of the 3-D NMNT. The proposed algorithm is found to offer substantial savings over the row-column approach in terms of arithmetic operations. Examples are given showing the validity of both transform and algorithm.
Author(s): Boussakta S, Alshibami O, Aziz M, Holt AGJ
Publication type: Article
Publication status: Published
Journal: IEE Proceedings - Vision, Image and Signal Processing
Year: 2001
Volume: 148
Issue: 2
Pages: 115-125
ISSN (print): 1350-245X
ISSN (electronic): 1359-7108
Publisher: IEEE
URL: http://dx.doi.org/10.1049/ip-vis:20010312
DOI: 10.1049/ip-vis:20010312
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