Published in Optical Society of America, Annual Meeting, vol.A4-13 pp. 84, Oct 1987.
We havce developed a new class of pyramid transform using quadrature mirror filter kernels. Unlike Gabor transforms, the basis functions are orthogonal and the coefficients are readily comptuted. Unlike ordinary pyramids, there is no increase in the number of samples needed to represent an image, and the sampling functxions are identical to the basis functions. Good localization can be achieved in space, spatial frequency, and orientation. We have derived QMF pyramids for square, quincunx and hexagonal decimation grids; each has its own set of kernls and its own advantages. By placing the representation in a pyramid structure one can achieve highly efficient computation. The pyramids should have uses in a variety of image processing and image coding tasks.