Pyramid (image processing): Difference between revisions

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'''Pyramids''' or ''''pyramid representation'''' is a type of [[Scale model|multi-scale]] [[Signal (information theory)|signal]] [[Knowledge representation|representation]] developed by the [[computer vision]], [[image processing]] and [[signal processing]] communities in which a signal or an image is subject to repeated smoothing and subsampling. Historically, pyramid representation is a predecessor to [[scale-space|scale-space representation]] and [[multiresolution analysis]].

==Pyramid generation==

There are two main types of pyramids; lowpass pyramids and bandpass pyramids. A ''lowpass pyramid'' is generated by first smoothing the image with an appropriate smoothing filter and then subsampling the smoothed image, usually by a factor of two along each coordinate direction. As this process proceeds, the result will be a set of gradually more smoothed images where in addition the spatial sampling density decreases level by level. If illustrated graphically, this multi-scale representation will look like a pyramid, from which the name has been obtained. A ''bandpass pyramid'' is obtained by forming the difference between adjacent levels in a pyramid, where in addition some kind of interpolation is performed between representations at different resolution, enabling the computation of differences.

==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'' stand out as a particularly useful and theoretically well-founded class (Crowley 1981; Lindeberg 1990, 1994).

==References==

* Burt, P.J. "Fast filter transforms for image processing", Computer Vision, Graphics and Image Processing, vol 16, pages 20-51, 1981.

* Burt, Peter and Adelson, Ted, "The Laplacian Pyramid as a Compact Image Code", IEEE Trans. Communications, 9:4, 532–540, 1983.

* Crowley, James "A representation for visual information", PhD thesis, Carnegie-Mellon University, Robotics Institute, Pittsburgh, Pennsylvania 1981.

*[http://www-prima.inrialpes.fr/Prima/Homepages/jlc/papers/Crowley-Sanderson-PAMI87.pdf Crowley, J. L. and Sanderson, A. C. "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.]

*[http://www-prima.inrialpes.fr/Prima/Homepages/jlc/papers/Crowley-ScaleSpace03.pdf Crowley, J, Riff O: Fast computation of scale normalised Gaussian receptive fields, Proc. Scale-Space'03, Isle of Skye, Scotland, Springer Lecture Notes in Computer Science, volume 2695, 2003.]