Based on the local statistics in a sliding window, the frost filter
works on preserving the edges while suppressing the noise. The Damping factor
which is an exponential damping is the key factor in controlling the smoothness
of the filter. When damping factor is small, the image tends to be smooth.

**ALGORITHM:**

**MATLAB CODE:**

%FROST FILTER

%LENNA IMAGE - SPECKLE
REDUCTION

% INPUT PARAMETERS - NOISY
IMAGE, DAMPING FACTOR, WINDOW SIZE

load('Noise_image1.mat')

ima_nse = double(ima_nse);

%Damping factor

Damp_fact = 1;

%window size

sz = [5,5];

%Preallocate the Output
Matrix

ima_fi = zeros(size(ima_nse));

if(mod(sz,2)~=1)

sz=sz+~mod(sz,2);

end

mn = round((sz-1)/2);

%Padding with zeros around
the border

EImg = padarray(ima_nse,mn);

[x,y]=
meshgrid(-mn(1,1):mn(1,1),-mn(1,2):mn(1,2));

S = sqrt(x.^2+y.^2);

for i = 1:size(ima_nse,1)

for j = 1:size(ima_nse,2)

%Local Window

K = EImg(i:i+sz(1,1)-1,j:j+sz(1,2)-1);

%Mean value of the pixels in the
local window

meanV = mean(K(:));

%variance of the pixels in the
local window

varV = var(K(:),1);

%Weight for each pixel in the
local window

B =
Damp_fact*(varV/(meanV*meanV));

Weigh = exp(-S.*B);

% Filtering

ima_fi(i,j) =
sum(K(:).*Weigh(:))./sum(Weigh(:));

end

end

figure,subplot(121),imagesc(ima_nse);colormap(gray);title('Original
Image');

subplot(122),imagesc(ima_fi);colormap(gray);title('After
Despeckling - Frost Filter');

**EXPLANATION:**

Here in the example given
above, the damping factor = 1 and the size is 5x5.

Let’s consider another
example, where damping factor =1 and the local window size is 11x11

The image becomes smooth
as well as the edges.

This is the parameter, S
that has the distance from centre of the pixel to its neighbours in the local
window. See that the distance at the centre for the centre pixel is zero, while
the distance from the centre to the adjacent pixel is 1 and the increase in
value based on the distance between the pixels is evident in the figure.

While in this example,
where damping factor = 3 and the local window size is 11x11, the edges are preserved.
By controlling the damping factor, a trade-off between the smoothness and
preservation of the edges can be done.