Pyramids or 'pyramid representation' is a type of multi-scale signal 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 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.
- 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.
- 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.
Lindeberg, T., "Scale-space for discrete signals," PAMI(12), No. 3, March 1990, pp. 234-254.
- Lindeberg, Tony, Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, 1994, ISBN 0-7923-9418-6
- Lindeberg, T. and Bretzner, L.: Real-time scale selection in hybrid multi-scale representations, Proc. Scale-Space'03, Isle of Skye, Scotland, Springer Lecture Notes in Computer Science, volume 2695, pages 148-163, 2003.
- Lowe, D. G., “Distinctive image features from scale-invariant keypoints”, International Journal of Computer Vision, 60, 2, pp. 91-110, 2004.