Median
Filter is used for noise reduction by removing salt and pepper noise.
The main idea of the median filter is replacing each pixel with the
average of neighboring pixels [5,7]. Fig. 3 indicates the result.
Figure 3 A, Gray image. B, Image after median filter.
Gaussian Filter
The Gaussian smoothing operator is a convolution operator that is used
to blur an image. Its kernel represents the shape of a Gaussian
bell-shaped [6,7]. Fig. 4 indicates the result. Gaussian filter can
be expressed as
\(I(X)=\frac{1}{2\pi\delta^{2}}\text{\ .\ }e^{-\frac{x^{2}+y^{2}}{2\delta^{2}}}\ .\ I(Y)\)(1)
where x is the distance from the origin in the horizontal axis, y is the
distance from the origin in the vertical axis, and \(\delta\) is
the standard
deviation of the Gaussian distribution.