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==Pyramid generation kernels==
A variety of different smoothing kernels have proposed for generating pyramids.<ref>Burt, P.J. "Fast filter transforms for image processing", Computer Vision, Graphics and Image Processing, vol 16, pages 20-51, 1981.</ref><ref name=Crowley1981>Crowley, James "A representation for visual information", PhD thesis, Carnegie-Mellon University, Robotics Institute, Pittsburgh, Pennsylvania 1981.</ref><ref>Burt, Peter and Adelson, Ted, "[http://web.mit.edu/persci/people/adelson/pub_pdfs/pyramid83.pdf The Laplacian Pyramid as a Compact Image Code]", IEEE Trans. Communications, 9:4, 532–540, 1983.</ref><ref>Crowley, J. and Parker, A.C, "A Representation for Shape Based on Peaks and Ridges in the Difference of Low Pass Transform", IEEE Transactions on PAMI, 6(2), pp 156-170, March 1984.</ref><ref>Crowley, J. L. and Sanderson, A. C. "[http://www-prima.inrialpes.fr/Prima/Homepages/jlc/papers/Crowley-Sanderson-PAMI87.pdf Multiple resolution representation and probabilistic matching of 2-D gray-scale shape]", IEEE Transactions on Pattern Analysis and Machine Intelligence, 9(1), pp 113-121, 1987.</ref><ref>P. Meer, E. S. Baugher and A. Rosenfeld "Frequency ___domain analysis and synthesis of image generating kernels", IEEE Transactions on Pattern Analysis and Machine Intelligence, vol 9, pages 512-522, 1987.</ref> 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.<ref name=Crowley1981/><ref>Lindeberg, Tony, "[http://www.nada.kth.se/~tony/abstracts/Lin90-PAMI.html Scale-space for discrete signals]," PAMI(12), No. 3, March 1990, pp. 234-254.</ref><ref>Lindeberg, Tony. [http://www.nada.kth.se/~tony/book.html Scale-Space Theory in Computer Vision], Kluwer Academic Publishers, 1994, ISBN 0-7923-9418-6</ref><ref>See the article on [[multi-scale approaches]] for a very brief theoretical statement</ref> 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 sometimes 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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