Gaussian Blur - standard deviation, radius and kernel size

Question

I've implemented a gaussian blur fragment shader in GLSL. I understand the main concepts behind all of it: convolution, separation of x and y using linearity, multiple passes to increase radius...

I still have a few questions though:

What's the relationship between sigma and radius?

I've read that sigma is equivalent to radius, I don't see how sigma is expressed in pixels. Or is "radius" just a name for sigma, not related to pixels?

How do I choose sigma?

Considering I use multiple passes to increase sigma, how do I choose a good sigma to obtain the sigma I want at any given pass? If the resulting sigma is equal to the square root of the sum of the squares of the sigmas and sigma is equivalent to radius, what's an easy way to get any desired radius?

What's the good size for a kernel, and how does it relate to sigma?

I've seen most implementations use a 5x5 kernel. This is probably a good choice for a fast implementation with decent quality, but is there another reason to choose another kernel size? How does sigma relate to the kernel size? Should I find the best sigma so that coefficients outside my kernel are negligible and just normalize?

Answer 1

What's the relationship between sigma and radius?

I think your terms here are interchangeable depending on your implementation. For most glsl implementations of Gaussian blur they use the sigma value to define the amount of blur. In the Gaussian blur definition the radius can be considered the 'blur radius'. These terms are in pixel space.

How do I choose sigma?

This will define how much blur you want, which corresponds to the size of the kernel to be used in the convolution. Bigger values will result in more blurring.

The NVidia implementation uses a kernel size of int(sigma*3).

You may experiment using a smaller kernel size with higher values of sigma for performance considerations. These are free parameters to experiment with, which define how many pixels to use for modulation and how much of the corresponding pixel to include in the result.

What's the good size for a kernel, and how does it relate to sigma?

Based on the sigma value you will want to choose a corresponding kernel size. The kernel size will determine how many pixels to sample during the convolution and the sigma will define how much to modulate them by.

You may want to post some code for a more detailed explanation. NVidia has a pretty good chapter on how to build a Gaussian Kernel. Look at Example 40-1.