Open In App
Related Articles

MATLAB – Ideal Lowpass Filter in Image Processing

Improve Article
Save Article
Like Article

In the field of Image Processing, Ideal Lowpass Filter (ILPF) is used for image smoothing in the frequency domain. It removes high-frequency noise from a digital image and preserves low-frequency components.

It can be specified by the function-

 $H(u, v)=\left\{\begin{array}{ll}1 & D(u, v) \leq D_{0} \\ 0 & D(u, v)>D_{0}\end{array}\right.$

D_{0} is a positive constant. ILPF passes all the frequencies within a circle of radius D_{0} from the origin without attenuation and cuts off all the frequencies outside the circle.

This D_{0} is the transition point between H(u, v) = 1 and H(u, v) = 0, so this is termed as cutoff frequency.

D(u, v) is the Euclidean Distance from any point (u, v) to the origin of the frequency plane, i.e,
 $D(u, v)=\sqrt{\left(u^{2}+v^{2}\right)}$


Step 1: Input – Read an image
Step 2: Saving the size of the input image in pixels
Step 3: Get the Fourier Transform of the input_image
Step 4: Assign the Cut-off Frequency D_{0}
Step 5: Designing filter: Ideal Low Pass Filter
Step 6: Convolution between the Fourier Transformed input image and the filtering mask
Step 7: Take Inverse Fourier Transform of the convoluted image
Step 8: Display the resultant image as output

Implementation in MATLAB:

% MATLAB Code | Ideal Low Pass Filter
% Reading input image : input_image 
input_image = imread('[name of input image file].[file format]');
% Saving the size of the input_image in pixels-
% M : no of rows (height of the image)
% N : no of columns (width of the image)
[M, N] = size(input_image);
% Getting Fourier Transform of the input_image
% using MATLAB library function fft2 (2D fast fourier transform)  
FT_img = fft2(double(input_image));
% Assign Cut-off Frequency  
D0 = 30; % one can change this value accordingly
% Designing filter
u = 0:(M-1);
idx = find(u>M/2);
u(idx) = u(idx)-M;
v = 0:(N-1);
idy = find(v>N/2);
v(idy) = v(idy)-N;
% MATLAB library function meshgrid(v, u) returns
% 2D grid which contains the coordinates of vectors
% v and u. Matrix V with each row is a copy 
% of v, and matrix U with each column is a copy of u
[V, U] = meshgrid(v, u);
% Calculating Euclidean Distance
D = sqrt(U.^2+V.^2);
% Comparing with the cut-off frequency and 
% determining the filtering mask
H = double(D <= D0);
% Convolution between the Fourier Transformed
% image and the mask
G = H.*FT_img;
% Getting the resultant image by Inverse Fourier Transform
% of the convoluted image using MATLAB library function 
% ifft2 (2D inverse fast fourier transform)  
output_image = real(ifft2(double(G)));
% Displaying Input Image and Output Image
subplot(2, 1, 1), imshow(input_image),
subplot(2, 1, 2), imshow(output_image, [ ]);

Input Image –


Last Updated : 22 Apr, 2020
Like Article
Save Article
Similar Reads