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A Prototype Filter Design Approach to Pyramid Generation
December 1993 (vol. 15 no. 12)
pp. 1233-1240

This paper presents a technique for image pyramid generation, in which the reduction (expansion) factor between layers is any rational number M/L. The image pyramid generation is modeled as an interpolation and filtering followed by a decimation. The model enables frequency domain analysis of the image pyramid, as well as convenient design of the generating 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 be produced by sampling one prototype low-pass filter with cutoff frequency at omega = pi /max(M,L). Using these polyphase filters, the frequency 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 factors to rational factors. Two types of low-pass filters are employed in this work for the prototype filter design: a binomial filter and an FIR linear phase filter. Illustrative examples are presented.

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Index Terms:
prototype filter design; image pyramid generation; reduction factor; expansion factor; interpolation; filtering; decimation; frequency domain analysis; polyphase filter network scheme; low-pass filter; polyphase filters; binomial filter; FIR linear phase filter; data compression; digital filters; filtering and prediction theory; frequency-domain analysis; image coding; low-pass filters
Citation:
M.G. Kim, I. Dinstein, L. Shaw, "A Prototype Filter Design Approach to Pyramid Generation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 12, pp. 1233-1240, Dec. 1993, doi:10.1109/34.250842
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