Within

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...

, in many cases only one

image An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...

with

noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...

is available, and averaging is then realized in a local neighbourhood. Results are acceptable if the noise is smaller in size than the smallest objects of interest in the image, but blurring of edges is a serious disadvantage. In the case of smoothing within a single image, one has to assume that there are no changes in the gray levels of the underlying image data. This assumption is clearly violated at locations of image edges, and edge blurring is a direct consequence of violating the assumption.

Description

Averaging is a special case of discrete convolution. For a 3 by 3 neighbourhood, the convolution mask ''M'' is:

M = \frac \begin1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1 \\
\end

The significance of the central pixel may be increased, as it approximates the properties of noise with a

Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

probability distribution:

M = \frac \begin1 & 1 & 1 \\
1 & 2 & 1 \\
1 & 1 & 1 \\
\end

M = \frac \begin1 & 2 & 1 \\
2 & 4 & 2 \\
1 & 2 & 1 \\
\end

A suitable page for beginners about matrices is at: https://web.archive.org/web/20060819141930/http://www.gamedev.net/reference/programming/features/imageproc/page2.asp The whole article starts on page: https://web.archive.org/web/20061019072001/http://www.gamedev.net/reference/programming/features/imageproc/

References

Signal processing Noise (graphics) Radio technology {{radio-comm-stub