Recursive, In-Place Algorithm For The Hexagonal Orthogonal Oriented Quadrature Image Pyramid
Andrew B. Watson · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
Pyramid image transforms have proven useful in image coding and pattern recognition. The Hexagonal orthogonal Oriented quadrature image Pyramid (HOP), transforms an image into a set of orthogonal, oriented, odd and even bandpass sub-images. It operates on a hexagonal input lattice, and employs seven kernels, each of which occupies a neighborhood consisting of a point and a hexagon of six nearest neighbors. The kernels consist of one lowpass and six bandpass kernels that are orthogonal, self-similar, and localized in space, spatial frequency, orientation, and phase. The kernels are first applied to the image samples to create the first level of the pyramid, then to the lowpass coefficients to create the next level. The resulting pyramid is a compact, efficient image code. Here we describe a recursive, in-place algorithm for computation of the HOP transform. The transform may be regarded as a depth-first traversal of a tree structure. We show that the algorithm requires a number of operations that is on the order of the number of pixels.