This is distinct from a difference-of-Gaussian operation that requires a much smaller kernel size for the Gaussian filter.

In fact, it can be understood as a smoothing of the Wigner quasiprobability distribution by a Gaussian filter:

Resolved sub-filter scales only exist when filters non-local in wave-space are used (such as a box or Gaussian filter).

Gaussian filter - minimum group delay; gives no overshoot to a step function.

Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time.

This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay.

The response value of the Gaussian filter at this cut-off frequency equals exp(-0.5) 0.607.

This makes the Gaussian filter physically unrealizable.

However, no amount of delay can make a Gaussian filter causal, because the Gaussian function is never zero.

For this, the image is convolved with Gaussian filters at different scales, and then the difference of successive Gaussian-blurred images are taken.