use 5 by 5 binomial filter and imfilter in matlab

To apply a 5x5 binomial filter to an image in MATLAB, you can use the function binomialFilter() which generates the 5x5 filter coefficients. Then, you can apply the filter to the image using the imfilter() function. Here is an example code:


main.m
% Load an example image
img = imread('pout.tif');

% Generate the 5x5 binomial filter coefficients
B = binomialFilter(5);

% Apply the filter using imfilter
filteredImg = imfilter(img, B);

% Display the original and filtered image
figure;
subplot(1,2,1); imshow(img); title('Original Image');
subplot(1,2,2); imshow(filteredImg); title('Filtered Image');
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The binomialFilter() function can be defined as follows:


main.m
function B = binomialFilter(n)
% Generate the binomial filter coefficients for a filter of size nxn
% Reference: https://www.cs.umb.edu/~marc/cs675/cvs/latex/ml/binomial_filter.m
B = zeros(n,n);
for i=1:n
    B(i,1) = 1;
    B(i,2) = i - 1;
    for j=3:n
        B(i,j) = ((i-1)*B(i,j-1)-(i-2)*B(i,j-2))/j;
    end
end
B = B/sum(sum(B)); % normalize the filter coefficients
end
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This function generates the filter coefficients by computing the binomial coefficients for each row of the filter, and then normalizes the filter so that the sum of its coefficients equals 1.

The imfilter() function applies the filter to the input image by convolving the filter kernel with the image intensity values at each pixel location. This results in a smoothed output image that reduces noise and sharpens edges.

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