Write a custom MATLAB script that performs spatial filtering with a kernel of size 𝑁 × 𝑁 without using imfilter.

implement a lowpass (smoothing) filter with three different kernel sizes, namely, 3 × 3, 5 × 5, and 7 × 7. Very importantly, the sum of kernel values must be equal to 1 for all three different cases. Manually implement zero-padding for each kernel size and iteratively produce a filtered image.

also use the same code to modify it so that it performs spatial filtering using zero-padding and the following 3 × 3 kernel:

[ -1 0 1

-1 0 1

-1 0 1]

Also perform Laplacian filtering in continuation to above code for 3x3 kernel:

[ 0 -1 0

-1 4 -1

0 -1 0]

[Matt J]

You have not posted enough for us to see that you have done 90% of this homework, nor told us which 10% you are asking for help with.

[Priyansh Pathak]

% Read images 1 and 2

img = imread('Xray_Bone.tiff');

X = im2gray(img);

X = double(X);

% Read Kernels

Kernel_1 = (1/9)*ones(3);

Kernel_2 = (1/25)*ones(5);

Kernel_3 = (1/49)*ones(7);

V=size(X);

for i=1:3
    
    img_out_i=[];
    
    U = size(Kernel_1);
    
    X_padded=zeros([V(1) + (U(1)-1), V(2) + (U(2)-1)]);
    
    disp(size(X_padded))
    
    m=floor(U(1)/2);
    
    n=floor(U(2)/2);
    
    X_padded([m:V(1)+m-1],[n:V(2)+n-1]) = X;
    
    % Perform convolution on image and selected kernel
    
    img_out_i = convolution3dLayer (X_padded, Kernel_1);
    
end

%%Display output images

figure('color','w')

subplot(1,3,1); imshow(img_out_i,[]); title('filter 1 output')

subplot(1,3,2); imshow(img_out_2,[]); title('filter 2 output')

subplot(1,3,3); imshow(img_out_3,[]); title('filter 3 output')

[yanqi liu]

may be use conv2 to compute

Answer 1

[Gyan Vaibhav]

Hi Priyansh,

I understand that you want to write MATLAB script that can perform spatial filtering on images with NxN filters also further use this perform Laplacian filtering without using MATLAB’s inbuilt “imfilter” function.

Your code looked alright but there were few areas of improvement.

1. The function “convolution3dLayer” you're using is not suitable for this task. It's used for creating a 3-D convolutional layer for a Convolutional Neural Network (CNN), not for image convolution. It can be replaced with a custom convolution function.
2. The loop is supposed to traverse over the different kernels, however due to a slight mistake it always uses the “kernel_1”.
3. Further, the outputs “img_out_2” and “img_out_3” are undefined.

Here is the modified code as per your requirements:

% Read images
img = imread('image.png');
X = im2gray(img);
X = double(X);

% Define Kernels
Kernel_1 = (1/9)*ones(3);
Kernel_2 = (1/25)*ones(5);
Kernel_3 = (1/49)*ones(7);
Kernel_custom = [-1 0 1; -1 0 1; -1 0 1];
Kernel_laplacian = [0 -1 0; -1 4 -1; 0 -1 0];

% Store kernels in a cell array for easy access
kernels = {Kernel_1, Kernel_2, Kernel_3, Kernel_custom, Kernel_laplacian};

V = size(X);
img_out = cell(1, length(kernels)); % Initialize output cell array

for i=1:length(kernels)
    kernel = kernels{i}; % Choose the kernel
    
    % Perform convolution on image and selected kernel
    img_out{i} = spatial_filter(X, kernel); % Use the previously defined function
end

% Display output images
figure('color','w')

subplot(2,3,1); imshow(img_out{1},[]); title('3x3 Lowpass Filtered Image')
subplot(2,3,2); imshow(img_out{2},[]); title('5x5 Lowpass Filtered Image')
subplot(2,3,3); imshow(img_out{3},[]); title('7x7 Lowpass Filtered Image')
subplot(2,3,4); imshow(img_out{4},[]); title('Custom Kernel Filtered Image')
subplot(2,3,5); imshow(img_out{5},[]); title('Laplacian Filtered Image')

% Define the spatial filter function
function filtered_img = spatial_filter(img, kernel)
[img_height, img_width] = size(img);
[kernel_height, kernel_width] = size(kernel);
pad_height = floor(kernel_height / 2);
pad_width = floor(kernel_width / 2);

padded_img = padarray(img, [pad_height, pad_width]);
filtered_img = zeros(size(img));

for i = 1:img_height
    for j = 1:img_width
        region = padded_img(i:i+kernel_height-1, j:j+kernel_width-1);
        filtered_img(i, j) = sum(sum(double(region) .* kernel));
    end
end
end

The changes I have made are:

1. Specified a function that does the convolution and takes care of padding.
2. Included the Laplacian and custom filters.
3. Fixed your loop and your output.

Hope this helps and resolves your issue.

Thanks

Gyan