Noise reduction is obtained by blurring the image using a smoothing filter. Blurring is used in pre-processing steps, such as the removal of small details from an image prior to object extraction and, bridging of small gaps in lines or curves.

The output or response of smoothing, the linear spatial filter is simply the average of the pixels contained in the neighborhood of the filter mask.

Since the smoothing spatial filter performs the average of the pixels, it is also called an averaging filter.

The smoothing filter replaces the value of every pixel in an image with the average value of the gray levels. So, this helps in removing the sharp transitions in the gray levels between the pixels. This is done because random noise typically consists of sharp transitions in gray levels.

Edges, which almost always are desirable features of an image, also are characterized by sharp transitions in gray levels. So, averaging filters have an undesirable side effect that they blur these edges.

One of the applications of smoothing spatial filters is that they help in smoothing the false contours that result from using an insufficient number of gray levels.

This is a smoothing spatial filter. This mask yields a so-called weighted average, which means that different pixels are multiplied with different coefficient values. This helps in giving much importance to some pixels at the expense of others.

The mask shown in the figure represents a 3×3 smoothing filter. The use of this filter yields the standard average of the pixels under the mask.

A spatial averaging filter or spatial smoothening filter in which all the coefficients are equal is also called a box filter.

We know that as the size of the filter used in smoothening the original image that is averaging filter increases then the blurring of the image. Since the second image is more blurred than the first image, the window size should be more than 9.

An important application of spatial averaging is to blur an image to get a gross representation of interesting objects, such that the intensity of the small objects blends with the background and large objects become easy to detect.

Order static filters are nonlinear smoothing spatial filters whose response is based on the ordering or ranking of the pixels contained in the image area encompassed by the filter, and then replace the value of the central pixel with the value determined by the ranking result.

The median filter belongs to order static filters, which, as the name implies, replaces the value of the pixel by the median of the grey levels that are present in the neighborhood of the pixels.

Median filters are used to remove impulse noises, also called salt-and-pepper noise because of their appearance as white and black dots in the image.

Isolated clusters of pixels that are light or dark with respect to their neighbors, and whose area is less than n²/2, i.e., half the area of the filter, can be eliminated by using an n×n median filter.

Spatial domain processes will be denoted by the expression g(x,y)=T[f(x,y)], where f(x,y) is the input image, g(x,y) is the processed image, and T is an operator on f, defined over some neighborhood of (x, y). In addition, T can operate on a set of input images, such as performing the pixel-by-pixel sum of K images for noise reduction.

The introduction to gray-level transformations shows three basic types of functions used frequently for image enhancement: linear (negative and identity transformations), logarithmic (log and inverse-log transformations), and power-law (nth power and nth root transformations). The identity function is the trivial case in which output intensities are identical to input intensities. It is included in the graph only for completeness.

The negative of an image with gray levels in the range[0, L-1] is obtained by using the negative transformation, which is given by the expression: s=L-1-r.

The general form of the log transformation: s=clog10(1+r)

where

c is a constant, and it is assumed that r ≥ 0.

Power-law transformations have the basic form: s=crγ where c and g are positive constants. Sometimes s=crγ is written as s=c.(r+ε)γ to account for an offset (that is, a measurable output when the input is zero).