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sat

What is G referring to here? Gaussian? For step 1 I would think we convolve with a sobelX/sobelY for the corresponding derivatives and step 3 a box filter to obtain the sums of the elements in the window.

motoole2

For step 1, $G^x_\sigma$ represents the derivative of a Gaussian (with standard deviation $\sigma$).

For step 3, $G_{\sigma'}$ represents a Gaussian (with standard deviation $\sigma'$). In practice, this could also be replaced with a box filter.