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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). Thus, given a two-dimensional image, we may apply the binomial filter (1, 2, 1) typically once or twice along each spatial dimension and then subsample the image. This operation proceeds as many times as desired, leading to a compact and efficient multi-scale representation. Today, with the increasing computational efficiency of [[CPU]]s, it is also feasible to use [[Gaussian filter]]s can also be used as smoothing kernels in the pyramid generation steps.
==Applications of pyramids==
In the early days of computer vision, pyramids were used as the main type of multi-scale representation. Today, this role has been taken over by [[scale-space]] representation, motivated by the more solid theoretical foundation to decouple the subsampling stage from the multi-scale representation, the more powerful tools for theoretical analysis as well as the ability to compute a representation at ''any'' scale thus avoiding the algorithmic problems of relating image representations at different levels of representation. Nevertheless, pyramids are still frequently used for expressing approximations to scale-space representation (Lindeberg and Bretzner 2003; Crowley and Riff 2003; Lowe 2004).
==References==
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