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-
is a positive constant. ILPF passes all the frequencies within a circle of radius from the origin without attenuation and cuts off all the frequencies outside 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 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:
Input Image –
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