Pyramid (image processing): Difference between revisions

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| pmid = 21869180

| doi = 10.1109/TPAMI.1984.4767500

}}</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 (see specifically Chapter 2 for an overview of Gaussian and Laplacian image pyramids and Chapter 3 for theory about generalized binomial kernels and discrete Gaussian kernels)</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 motivated by specific requirements, intermediate scale levelsl
A mayLaplacian also be generated where the subsampling stagepyramid is sometimesvery left out, leadingsimilar to ana ''oversampled'' or ''hybridGaussian pyramid''.<ref name=LinBre03-ScSp/>but Withsaves the increasingdifference computational efficiencyimage of [[CPU]]sthe availableblurred today,versions itbetween iseach inlevels. someOnly situationsthe alsosmallest feasiblelevel tois usenot widera supportdifference [[Gaussianimage, filter]]sto asenable smoothing kernels in the pyramid generation steps.recons

===Gaussian pyramid===

In a Gaussian pyramid, subsequent images are weighted down using a Gaussian average ([[Gaussian blur]]) and scaled down. Each pixel containing a local average that corresponds to a pixel neighborhood on a lower level of the pyramid. This technique is used especially in [[texture synthesis]].

===Laplacian pyramid===

A Laplacian pyramid is very similar to a Gaussian pyramid but saves the difference image of the blurred versions between each levels. Only the smallest level is not a difference image, to enable reconstruction of the high resolution image using the difference images on higher levels. This technique can be used in [[image compression]].<ref>

Peter J. Burt and Edward H. Adelson.

[http://persci.mit.edu/pub_pdfs/pyramid83.pdf "The Laplacian Pyramid as a Compact Image Code"].

IEEE Transactions on Communications.

{{doi|10.1109/TCOM.1983.1095851}}.

1983.

</ref>