Solution:

Smoothing filters are used for blurring and for noise reduction.

Blurring is used in processing tasks such as the removal of small details from an image The output of a smoothing linear spatial filter is simply the average of the pixels contained in the neighborhood These filters sometimes are called Low pass averaging filters.

By replacing the value of every pixel in an image with the average of the intensity levels in the neighborhood defined. by the filter mask-.

This process results in an image with a reduced "sharp" transition in intensive.

Because random noise typically consists of sharp transitions in intensity levels, the most obvious application of smoothing is noise reduction.

However edges also are characterized by sharp intensity transitions, so averaging they blur edges.

The use of the following smoothing filter mask gives the standard average of the pixels.

This can be seen by substituting the coefficient of the mask into the equation.

$$ R=\frac{1}{a} \sum_{i=1}^q z_i $$

which is the average of the intensity levels of the pixels in the $3 \times 3$ neighborhood defined by the mask.

$$ \begin{array}{|l|l|l|} \hline 1 & 1 & 1 \\ \hline 1 & 1 & 1 \\ \hline 1 & 1 & 1 \\ \hline \end{array} $$

A spatial averaging filter in which all coefficients are equal sometimes is called a bor filter.