Fast Fourier Transform for Hexagonal Aggregates

Authors:
Jaime L. Zapata;Gerhard X. Ritter
Affiliations:
Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA. jlz@cise.ufl.edu;Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA. ritter@cise.ufl.edu
Venue:
Journal of Mathematical Imaging and Vision
Year:
2000

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Abstract

Hexagonal aggregates are hierarchicalarrangements of hexagonal cells. These hexagonal cells may beefficiently addressed using a scheme known as generalizedbalanced ternary for dimension 2, or GBT_2. The objects ofinterest in this paper are digital images whose domains are hexagonalaggregates. We define a discrete Fourier transform (DFT) forsuch images. The main result of this paper is a radix-7,decimation-in-space fast Fourier transform (FFT) for imagesdefined on hexagonal aggregates. The algorithm has complexityN log_7 N. It is expressed in terms of the p-product, ageneralization of matrix multiplication. Data reordering (also knownas shuffle permutations) is generally associated with FFT algorithms.However, use of the p-product makes data reorderingunnecessary.