Why Gauss filter chooses such values?

Gauss filter is a famous image denoising tool in image processing domain. I saw lots of opensource software choose the template like this:

enter image description here

Where do these value come from?

Solution

You linked the Answer yourself. These values are a discrete representation of the Gaussian Function.

The 2D Gaussian looks like this:

enter image description here

To get the Filter Values you evaluate the 2D-Gaussian Function at the discrete x-y Position corresponding to your Kernel Size and sigma.

On this website you can find a detailed explanation of the Gaussian Filter.