Ideal Low Pass Filters in Image Preprocessing

Ideal Low Pass Filter (ILPF) work over images transformed into frequency domain by using transformation such as Fourier transform, and act as sieve that allows low frequency components to pass through and blocks the large frequency component's. This post is about exploring the overview of ILPF in image preprocessing and their working so, lets start with definition.

What is Ideal Low Pass Filter?

ILPF is frequency domain filter that works over sharp cutoff frequency means the frequency components which are below Do (D knot) are passed through filter and components larger than that are blocked.

Numerical Example and step for Ideal Low Pass Filter

Let’s have image :

Transform the image using 2D Discrete Fourier Transform (DFT) :

Matrix after DFT:

Consider cutoff frequency D0=1 . The ILPF transfer function H(u,v) for a 3x3 image with the origin at the center is:

Multiply H(u,v) and F(u,v) in order to apply ILPF