A note on shrinking and expanding operations in pyramids

Abstract Simple pyramid algorithms are described that, in O(k) steps, shrink or expand the 1's in a binary image by 2k − 1 (k = 1,2, …) and resample the results at intervals of 2k. For a one-dimensional image, the results can be computed without resampling provided the kth step is allowed to involve O(k) computation; but in two dimensions, O(2k) computation would be required, so that the pyramid has no advantages over a mesh. For grayscale images (with local Min and local Max playing the roles of shrinking and expanding), the resampled computation is still straightforward, but the unresampled computation cannot be done economically even in the one-dimensional case.