MATLAB – Ideal Highpass Filter in Image Processing

22 Apr, 2020
In the field of Image Processing, Ideal Highpass Filter (IHPF) is used for image sharpening in the frequency domain. Image Sharpening is a technique to enhance the fine details and highlight the edges in a digital image. It removes low-frequency components from an image and preserves high-frequency components.
This ideal highpass filter is the reverse operation of the ideal lowpass filter. It can be determined using the following relation- where,  is the transfer function of the highpass filter and  is the transfer function of the corresponding lowpass filter.
The transfer function of the IHPF can be specified by the function-Where,
 is a positive constant. IHPF passes all the frequencies outside of a circle of radius  from the origin without attenuation and cuts off all the frequencies within the circle.
This  is the transition point between H(u, v) = 1 and H(u, v) = 0, so this is termed as cutoff frequency.
 is the Euclidean Distance from any point (u, v) to the origin of the frequency plane, i.e, 
Approach:
Step 1: Input – Read an imageStep 2: Saving the size of the input image in pixelsStep 3: Get the Fourier Transform of the input_imageStep 4: Assign the Cut-off Frequency Step 5: Designing filter: Ideal High Pass FilterStep 6: Convolution between the Fourier Transformed input image and the filtering maskStep 7: Take Inverse Fourier Transform of the convoluted imageStep 8: Display the resultant image as output
Implementation in MATLAB:
% MATLAB Code | Ideal High 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 = 10; % one can change this value accordingly  % Designing filteru = 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 DistanceD = sqrt(U.^2+V.^2);  % Comparing with the cut-off frequency and % determining the filtering maskH = double(D > D0);  % Convolution between the Fourier Transformed image and the maskG = 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 Imagesubplot(2, 1, 1), imshow(input_image),subplot(2, 1, 2), imshow(output_image, [ ]);
Input Image –
Output:
Image-Processing
MATLAB
Advanced Computer Subject
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