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-
- 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,
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:
Input Image –
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