Application of convolution in image processing


There is such an image, you can see that there are many noise points on the image:

High frequency signal is like a mountain on the ground:

It looks conspicuous.

One of the ways to smooth the mountain is to cut off some soil and fill it around. In mathematical terms, it is to average the height around the mountain peak.

After smoothing, we get:




4.2 calculation

Convolution can help to achieve this smoothing algorithm.

The original image with noise can be transformed into a matrix:

Then use the following average matrix (note that the processing of the original image actually uses the normal distribution matrix, here for simplicity, the arithmetic average matrix) to smooth the image:

Remember the algorithm just mentioned, average the high frequency signal with the surrounding values to smooth the mountain.

For example, if I want to smooth point a1,1a1,1, in the matrix, I will take the points near point a1,1a1,1 to form the matrix F, and then I will convolute them with G and fill them back






It should be noted that in order to use convolution, G is the same dimension as F, but the subscript is a little different: