Image filtering by convolution

Abstract

Image filtering is a common technique used in digital image processing that can be used to take a picture appear differently aesthetically. Noise, also known as distracting visual artifacts, can lower the overall quality of a picture, which is why image improvement techniques are required to fix the problem. It can be utilized in a variety of ways, including smoothing, sharpening, reducing noise, and detecting borders, to name a few. In this piece, we will be using convolutional techniques to correct the images that were messed up. The first thing that needs to be done is a point-by-point multiplication of the frequency domain representation of the picture that's being entered through a black image that has a small white rectangle in the mid of it. This is the first step. Only the lowest harmonics are kept after we apply a filter that gets rid of the higher ones. Because the high frequencies in the input picture are filtered out, the special domain of the image that is produced should look like a blurrier variation of the original picture. Therefore, a greater degree of detail preservation is indicated when the white rectangle W is larger because this indicates that more high-frequency components of I have been preserved.