Some neighborhood operations work with the values of the image
pixels in the neighborhood and
the corresponding values of a sub image that has the same
dimensions as the neighborhood. The sub image is called a filter, mask, kernel,
template, or window, with
the first three terms being the most prevalent terminology. The values in a
filter sub image are referred to as coefficients, rather
than pixels. The process consists simply of moving the filter mask from
point to point in an image. At each point (x, y), the response of the filter at
that point is calculated using a predefined relationship.
Smoothing Spatial Filters divided into two types 
1. Smoothing Linear Filters 
a) Average Filter
b) Weighted Filter
2. Smoothing NonLinear Filters 
a) Median Filter
I. Average Filtering:
The output of a smoothing, linear spatial filter is simply the
average of the pixels contained in the neighborhood of the filter mask. These
filters sometimes are called averaging filters. For reasons explained in they also
are referred to a low pass filters. The idea behind smoothing filters is
straightforward. By replacing the value of every pixel in an image by the
average of the gray levels in the neighborhood defined by the filter mask, this
process results in an image with reduced “sharp” transitions in gray levels.
Because random noise typically consists of sharp transitions in gray levels,
the most obvious application of smoothing is noise reduction.
Average Filter mask is as follows:
MATLAB Code:
Code Output:
Code Output:
MATLAB Code:
% Read Image for Noise Addition
img=imread('lena.bmp');
% Add Noise
Noi_img = imnoise(img,'salt & pepper', 0.02);
% Mask Definition
f=1/9*[1,1,1;1,1,1;1,1,1];
% Apply filter2 function
de_noi=filter2(f,Noi_img);
figure;
subplot(1,3,1);imshow(img);title('Original image')
subplot(1,3,2);imshow(Noi_img);title('Noisy image')
subplot(1,3,3);imshow(uint8(de_noi));title('Denoised image')

II. Weighted Filtering:
The second mask is a little more interesting. This mask yields
a socalled weighted
average, terminology used to indicate that pixels are multiplied by
different coefficients, thus giving more importance (weight) to some pixels at
the expense of others. In the mask the pixel at the center of the mask is
multiplied by a higher value than any other, thus giving this pixel more
importance in the calculation of the average.
Weighted Filter mask is as follows:
MATLAB Code:
% Read Image for Noise Addition
img=imread('lena.bmp');
% Add Noise
Noi_img = imnoise(img,'salt & pepper', 0.02);
% Mask Definition
f=1/16*[1,2,1;2,4,2;1,2,1];
% Apply filter2 function
de_noi=filter2(f,Noi_img);
figure;
subplot(1,3,1);imshow(img);title('Original image')
subplot(1,3,2);imshow(Noi_img);title('Noisy image')
subplot(1,3,3);imshow(uint8(de_noi));title('Denoised image')

III. Median Filtering:
The bestknown example in this category is the median filter, which, as its name implies, replaces the value of a pixel by
the median of the gray levels in the neighborhood of that pixel (the original
value of the pixel is included in the computation of the median). Median
filters are quite popular because, for certain types of random noise, they
provide excellent noisereduction capabilities, with considerably less blurring
than linear smoothing filters of similar size. Median filters are particularly
effective in the presence of impulse
noise, also called saltandpepper
noise because of its appearance as white and black dots superimposed
on an image.
MATLAB code:
% Read Image for Noise Addition
img=imread('lena.bmp');
% Add Noise
Noi_img = imnoise(img,'salt & pepper', 0.02);
% Apply medfilt2 function
de_noi=medfilt2(Noi_img,[3 3]);
figure;
subplot(1,3,1);imshow(img);title('Original image')
subplot(1,3,2);imshow(Noi_img);title('Noisy image')
subplot(1,3,3);imshow(uint8(de_noi));title('Denoised image')

Comparison Between Filters:
Parameters

Average
Filter

Weighted
Filter

Median
Filter

Noise
Reduction

Reduces Noise but it introduces blurring effect at edges.

Blurring effect is less as compared with Average filter

Blurring effect is less as compared with Average filter

Percentage
of noise Reduction

100% noise Not Reduced

100% noise Not Reduced

Almost 100% noise reduced.

Size of
Filter

As we increase the size of the filter mask, Noise reduces but
blurring effect increases.

As we increase the size of the filter mask, Noise reduces but
blurring effect increases.

As we increase the size of the filter mask, 100% of Noise reduces
but blurring effect at edges increases.

Mask

1/9x[1,1,1;1,1,1;1,1,1]

1/16x[1,2,1;2,4,4;1,2,1]

Pixel value is replaced by median value of neighborhood.

MATLAB
Function

filter2(mask,Noisy_img)

filter2(mask,Noisy_img)

medfilt2(Noisy_img,[3 3])

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