Abstract

We have 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 computed. Unlike ordinary pyramids, there is no increase in the number of samples needed to represent an image, and the sampling functions 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 kernels and its own advantages. By placing the representation in a pyramid structure one can achieve highly efficient computation.

© 1987 Optical Society of America