George,

The number 0.36067 comes from how the spatial smoothing is implemented.

With a smoothing with Gaussian kernel N(0, Sigma^2), each voxel gets a new value with weighted average of its neighbors, and the weights are calculated based on the Gaussian distribution at that voxel.

Other than Sigma^2, another way to express the shape of Guassian distribution is its Full Width at Half Maximum (FWHM). A little mathematical derivation would reveal the following relationship between Sigma and FWHW:

FWHM = sigma * sqrt(8*log(2)) (1)

The Gaussian density function is usually expressed as:

exp(-x^2/(2*Sigma^2))/(Sigma*sqrt(2*Pi)) (2)

If we replace Sgima in (2) in terms of FWHW according to (1), we have

exp(-x^2/(2*FWHW*FWHW/(8*log(2)))/(FWHW*sqrt(2*Pi)/(sqrt(8*log(2)) ) (3)

Compared to the expression in the example you saw (-1filter_expr 12.0 'exp(-r*r/36.067)'\n") with (3), you can see

2/(8*log(2)) = 0.36067

This is how 0.36067 shows up in the smoothing processing.

Gang