Hexagonal image processing

The author describes the development of the underlying theory of processing hexagonally sampled digital images. He shows a direct form of both the FFT (fast Fourier transform) and the FWT (fast Walsh transform) as applied to a hexagonal lattice of data points. Advantages spring from a reduction in the number of data locations and a reduction in computational load per data point. The complete signal flow graph for a minimal hexagonal kernel for both the FFT and the FWT is shown. The derived transforms were implemented in software and compared to the standard 2-D FFT on standard images in the image processing laboratory. It was found that the hexagonal sampling of the image at a lower resolution retained the necessary resolution as required for the rest of the image software