Gaussian blur in ImageJ
This filter uses convolution with a Gaussian function for smoothing. Sigma is the radius of decay to exp(-0.5) ~ 61%, i.e. the standard deviation sigma of the Gaussian (this is the same as in Photoshop, but different from earlier versions of ImageJ, where a value 2.5 times as much had to be entered.
Like all ImageJ convolution operations, it assumes that out-of-image pixels have a value equal to the nearest edge pixel. This gives higher weight to edge pixels than pixels inside the image, and higher weight to corner pixels than non-corner pixels at the edge. Thus, when smoothing with very high blur radius, the output will be dominated by the edge pixels and especially the corner pixels (in the extreme case, with a blur radius of e.g. 1e20, the image will be raplaced by the average of the four corner pixels).
For increased speed, except for small blur radii, the lines (rows or columns of the image) are downscaled before convolution and upscaled to their original length thereafter.