# Gaussian Low Pass Filter in Image -Preprocessing

Imagine you have a sharp, clear photograph that you place behind a piece of frosted glass. When you look at the photo through the frosted glass, the image appears blurred, Gaussian low pass filter works like this frosted glass. This blurring happens because the frosted glass scatters light in such a way that sharp edges and fine details are smoothed out, while overall shapes and regions of similar color are preserved, similar to that Gaussian low pass filter also preserved the color and regions just smoothed details.

## What is Gaussian low pass filter ?

Gaussian low pass filter (GLPF) uses bell-shaped curve as working principle to attenuates high-frequency components and preserving the low- frequency components, that applies the smoothing effect over the image and less ringing effect than Butterworth low pass filters.

**Mathematical representation**

Where D0 (knot) represents the cutoff frequency and D(u,v) is given by :

## Python implenentation example

Let’s apply Gaussian filter over a noisy image for noise reduction :