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==Pyramid generation kernels==
A variety of different smoothing kernels have proposed for generating pyramids (Burt 1981; Crowley 1981; Burt and Adelson 1983; Crowley and Sanderson 1984; Meer et al 1987). Among the suggestions that have been given, the ''binomial kernels'' arising from the [[binomial coefficient]]s stand out as a particularly useful and theoretically well-founded class (Crowley 1981; Lindeberg 1990, 1994) (see the article on [[multi-scale approaches]] for a very brief theoretical statement). Thus, given a two-dimensional image, we may apply the (normalized) binomial filter (1/4, 1/2, 1/4) typically twice or more along each spatial dimension and then subsample the image by a factor of two. This operation may then proceed as many times as desired, leading to a compact and efficient multi-scale representation. If motivatived by specific requirements, intermediate scale levels may also be generated where the subsampling stage is left out, leading to an ''oversampled'' or ''hybrid pyramid''. With the increasing computational efficiency of [[CPU]]s available today, it is in some situations also feasible to use wider support [[Gaussian filter]]s as smoothing kernels in the pyramid generation steps.
==Applications of pyramids==
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