This software implements median, mean, and Gaussian filtering.
Median Filtering
Median filtering is needed to remove impulse noise from an image. A pixel intensity is replaced with the
median of pixel intensities within a window centered at that pixel. If a part of the window falls outside the
image, intensities within the portion of the window inside the image is used. Circular windows are used to
make smoothing independent of the image orientation. An example of median filtering b y this software is
given below.
Median Filtering
Median filtering is needed to remove impulse noise from an image. A pixel intensity is replaced with the
median of pixel intensities within a window centered at that pixel. If a part of the window falls outside the
image, intensities within the portion of the window inside the image is used. Circular windows are used to
make smoothing independent of the image orientation. An example of median filtering b y this software is
given below.
| (a) (b) |
Fig. 1. (a) An image containing impulse noise. (b) Smoothing the image by median filtering using a
filter of radius 1 pixel.
filter of radius 1 pixel.
Mean Filtering
Mean filtering is image averaging and the value at a pixel in the output is equal to the average of
values within a circular window centered at the pixel in the input. The window size determines the
neighborhood size where averaging is performed. As the window size is increased, more noise is
removed, but that at the same time blurs the image more. An example of mean filtering by this method
is given below.
Mean filtering is image averaging and the value at a pixel in the output is equal to the average of
values within a circular window centered at the pixel in the input. The window size determines the
neighborhood size where averaging is performed. As the window size is increased, more noise is
removed, but that at the same time blurs the image more. An example of mean filtering by this method
is given below.
| (a) (b) |
Fig. 2. (a) An image containing zero-mean noise. (b) Image obtained by mean filtering using a filter
of radius 4 pixels.
of radius 4 pixels.
Gaussian Filtering
A Gaussian is an ideal filter in the sense that it reduces the magnitude of high spatial frequencies in
an image proportional to their frequencies. That is, it reduces magnitude of higher frequencies more.
This will be at the cost of more computation time when compared to mean filtering. A Gaussian
extends to infinity in all directions, but because it approaches zero exponentially, it can be truncated
three or four standard deviation away from its center without affecting the result noticeably. Speed up
is achieved by splitting a 2-D Gaussian into two 1-D Gaussians, G(x,y) = G(x) G(y), and carrying out
filtering in 1-D, first row by row and then column by column. An example of Gaussian filtering is given
below.
A Gaussian is an ideal filter in the sense that it reduces the magnitude of high spatial frequencies in
an image proportional to their frequencies. That is, it reduces magnitude of higher frequencies more.
This will be at the cost of more computation time when compared to mean filtering. A Gaussian
extends to infinity in all directions, but because it approaches zero exponentially, it can be truncated
three or four standard deviation away from its center without affecting the result noticeably. Speed up
is achieved by splitting a 2-D Gaussian into two 1-D Gaussians, G(x,y) = G(x) G(y), and carrying out
filtering in 1-D, first row by row and then column by column. An example of Gaussian filtering is given
below.
| (a) (b) |
Fig. 3. (a), (b) Smoothing the image shown in Fig. 2a by Gaussian filters of standard deviations 2
and 4 pixels, respectively.
and 4 pixels, respectively.
To obtain a license for this software, please follow this link =>
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| Image Smoothing |
| Image Registration and Fusion Systems |
