Let $h_j$ denote the image reconstruction filter of pixel $j$. I'm estimating the color value $$I_j=\int h_jf\:{\rm d}\mu$$ of the $j$th pixel (see [Veach, Section 8.2]) by an asymptotically consistent estimator whose asymptotic variance is given by $\sigma^2_j$. (This has to be understood in a component-wise sense, i.e. $\sigma_j^2$ is a 3-dimensional vector whose $i$th component is the asymptotic variance of the estimate of the $i$th component of $I_j$.
Question 1: I want to compare different estimators which lead to different asymptotic variances and would like to visualize that one is superior to another (with respect to variance reduction). How can I do that? Simply writing the variances into an image doesn't seem to be sensible. (The problem is the scale of the values.)
Question 2: For simplicity, assume a box filter with radius $\frac12$ so that the computation of $I_j$ only involves the $j$th pixel. Instead of considering the variances of each pixel, I've seen that we could consider the variances of a "local window" (for example a $3\times 3$ pixel window). Is this a better or worse metric for the total variance of the image?