What is the optimal radius of gaussian distribution for determining pixel colour? Using a gaussian distribution of points on an image plane to calculate a pixel value, what radius/standard deviation will give the most information in the final image? Too large a radius gives a blurred image, and too small a radius neglects information that is smaller than a pixel so that it does not contribute to the final image. Where is the optimal compromise? Is there a single answer to this question or are there circumstances under which it can vary?

I'm thinking of this in relation to raytracing but I imagine it will apply equally to things like downsizing an image. Where the answers would differ, I am interested in what applies when sampling a continuous image plane, so that the positions of pixels in a larger image cannot be used to determine an optimal radius.
I'm not sure that there's a truly optimal radius&mdash;it's going to be a subjective matter based on what the image looks like.  As you say, too large a radius results in blurring and too small a radius results in aliasing.

I like to set sigma = 0.5 px, so that the overall radius is about 1.5 px (since the Gaussian has the majority of its weight within ±3 sigma of its mean).  In my experience that gives a good trade-off between blurring and aliasing, but that's just my taste, not based on any objective considerations.

By the way, as part of a blog post on antialiasing I wrote last year (which was based on an answer I posted on the previous incarnation of this site!), I tested a variety of antialiasing kernels against a synthetic test image and came out with 0.5 px Gaussian as my subjective favorite.