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MATLAB – Ideal Highpass Filter in Image Processing
• Last Updated : 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 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 Step 5: Designing filter: Ideal High 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 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: Attention reader! Don’t stop learning now. Get hold of all the important CS Theory concepts for SDE interviews with the CS Theory Course at a student-friendly price and become industry ready.

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