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# What Is a Gaussian Pyramid?

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• Written By: Andrew Kirmayer
• Edited By: Shereen Skola
• Last Modified Date: 12 February 2017
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A Gaussian pyramid is a series of images, typically processed by a computer, which are often continuously regenerated. When one image is blurred and a subset of it is produced, a set of pictures with one smaller than the last is generally the result of the computation. The pixels, or smallest individual parts of an image, usually take up more average content than the ones in the previous image; generally, pixels correspond to different levels of a pyramid, the top part representing the original picture, and the lower levels representing successive images.

Various image processing techniques involve using Gaussian pyramid type calculations. Texture synthesis of computer graphics is one application, while computer vision applications often use the principle as well. The first level of the pyramid, called level k, is usually first processed by generating a Gaussian blur, before a sub-sample from within an image is generated; the next stage is generally called level k+1. A process called convolution is often performed during this stage, which typically involves the averaging of the intensity in a certain part of an image.

Computing each step of the Gaussian pyramid generally requires a series of mathematical formulas. These integrate principles of trigonometry, derivatives, and functions; long equations can be used to solve problems related to image processing. Texture is one aspect that is addressed by computer systems, because it often has regular patterns that repeat, and there are various other types of patterns as well. A Gaussian pyramid is typically used for gray-scale images, but it can be applied to different parts of the color spectrum also.

The concept is similar to the Laplacian pyramid, which refers more to the clustering of points on graphs. In the case of an image, these points can correspond to the pixels. Computer software is often used to perform the calculations needed to produce the images associated with a Gaussian pyramid. The programming code is typically designed to let the software automatically do the math while an image is generated. Such mathematical calculations are called algorithms and can be used to alter the image pixels; properties that are wanted can be preserved, while others that are undesirable can be removed.

Various methods of image filtering can include processing techniques associated with the Gaussian pyramid. Linear filtering is often used, while images with corrupted data can be processed by using non-linear filters to remove noise, or distortions produced by unwanted data. The Gaussian pyramid technique can be used multiple times on the same image, which typically makes it suitable for use with sophisticated computer graphics programs.