Frequency domain analysis and synthesis of image pyramid generating kernels

Construction of image pyramids is described as a two-di-mensional decimation process. Frequently employed generating kernels are compared to the optimal kernel that assures minimal information loss after the resolution reduction, i.e., the one corresponding to an ideal low pass filter. Physically realizable, optimal generating kernels are presented. The amount of computation required for generation of the image pyramid can be reduced significantly by employing half-band filters as components of the optimal kernel. Image pyramids generated by the optimal kernel show a better command of details than the ones generated by a simple 4 × 4 averaging, or a computationally equivalent kernel.