A PROTOTYPE FILTER DESIGN APPROACH TO PYRAMID GENERATION

This paper presents a technique for image pyramid generation, in which the reduction (expansion) factor between layers is any rational numbe r M/L. The image pyramid generation is modeled as an interpolation and filtering followed by a decimation. The model enables frequency domai n analysis of the image pyramid, as well as convenient design of the g enerating kernels. L(M) generating kernels are necessary to produce an image pyramid with reduction (expansion) factor M/L(L/M). A polyphase filter network scheme is used where the L(M) generating kernels can b e produced by sampling one prototype low-pass filter with cutoff frequ ency at omega = pi/max[M,L]. Using these polyphase filters, the freque ncy content of pyramid image decompositions can be adjusted with great flexibility. A systematic procedure is presented here for specifying the relative positions of spatial samples in successive pyramid levels -a complication that arises when generalizing from integer reduction f actors to rational factors. Two types of low-pass filters are employed in this work for the prototype filter design: a binomial filter and a n FIR linear phase filter. Illustrative examples are presented.