Mg. Kim et al., A PROTOTYPE FILTER DESIGN APPROACH TO PYRAMID GENERATION, IEEE transactions on pattern analysis and machine intelligence, 15(12), 1993, pp. 1233-1240
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.