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I want to plot the Gaussian filter of pbrt-v4 with a radius $(100,100)$ and a standard deviation ($\sigma$) of $0.5$.

I would expect something like this:

enter image description here

When I plot the pbrt-v4 Gaussian filter with radius $(100,100)$ and $\sigma=0.5$ I get:

enter image description here

Is the 2nd plot correct? I varied the radius form $1$ to $1000$ but the the filter size changes only 2 pixels in total (I get a similar results). Any ideas? How does the correct plot look like?

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You probably want to set sigma to be a fraction of the radius, rather than a fixed value. Sigma controls the actual shape of the filter, while radius just controls how far out the filter gets cut off (as Gaussians truly have infinite radius, so we have to cut them off somewhere to use them in practice). With sigma set to 0.5, you're making a filter that's very sharply peaked within a radius of 0.5 pixels, which is consistent with the image you're getting.

Instead, try setting sigma = 0.25 or 0.3 times the radius. Or alternatively, make sigma your main parameter and then set the radius to 3 or 4 times sigma.

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