Recursive, In-Place Algorithm For The Hexagonal Orthogonal Oriented Quadrature Image Pyramid

Andrew B. Watson

doi:10.1117/12.960468

5 September 1989 Recursive, In-Place Algorithm For The Hexagonal Orthogonal Oriented Quadrature Image Pyramid

Andrew B. Watson

Proceedings Volume 1099, Advances in Image Compression and Automatic Target Recognition; (1989) https://doi.org/10.1117/12.960468
Event: SPIE 1989 Technical Symposium on Aerospace Sensing, 1989, Orlando, FL, United States

Abstract

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.

Citation Download Citation

Andrew B. Watson "Recursive, In-Place Algorithm For The Hexagonal Orthogonal Oriented Quadrature Image Pyramid", Proc. SPIE 1099, Advances in Image Compression and Automatic Target Recognition, (5 September 1989); https://doi.org/10.1117/12.960468

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