# Convolution of an Image with Gaussian sigma = 1

I'm new to image processing and I've been testing out different Gaussian blur filters.

Out of curiosity, I generated an object that is a 2D Gaussian with sigma = 1.

I convolved this object with a Gaussian of sigma = 1, and while their individual pixel values are different they look very nearly the same. I then changed the sigma of my Object to 5 (in both x and y directions) and found that convolution with a Gaussian of sigma = 1 gave the same result. Is there something deep going on here, or is a Gaussian of sigma = 1 just very weak?

• Please, add the image file as attachment. Did you tried to code? – Jose Enrique Calderon Nov 26 '18 at 3:01
• I suggest that you try the same thing in one dimension first. Then you may see what's happening more clearly. – bill s Nov 26 '18 at 4:28
• Basically, a Gaussian with sigma=5 convolved with a Gaussian with sigma=1 equals a Gaussian with sigma=Sqrt[5^2 + 1^2] ~= 5.1. So they should look similar. You can find a proof here: en.wikipedia.org/wiki/… – Niki Estner Nov 26 '18 at 7:35