Standard Deviation in Gaussian Blur I have a function that performs gaussian blur on image for some specific $\sigma$ (the standard deviation).

It first computes kernel of size $\lceil 3\sigma \rceil$ and then performs convolution with that kernel.

However, I would like to specify blurring radius in pixels rather than $\sigma$.

I suppose that the blur radius (in pixels) is just $\sigma^{2}$ as this denotes variance of a random variable.

Is that right? Can the same thought be extended to 2D?

UPDATE:

The problem is that I need to do things like building a gaussian pyramid (successively blurred and downsampled image).

When the image gets downsampled to 1/2 of its width, I suppose I need a gaussian blur of radius 2 pixels ($\sigma=\sqrt{2}$ ?). And for 1/4 subsampling, I would need blur of 4 pixels ($\sigma=2 ?)$... But I am not sure about that...
Yes, you can always use pixel units for $\sigma$. In 2-D you will have $\sigma_X$ and $\sigma_Y$.