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3. Difference of Gaussians
Letâs shift a bit our point of view; what if, instead of subtracting a blurred version from the untouched original, the subtraction is between two differently blurred originals? Have a look to the graph before we investigate the why of such a move with GBs:
(Fig 3.1) Intensity transition and Difference of Gaussians.
The concept behind the Difference of Gaussians (DoG) is quite simple: noise is usually high frequency spatial information, and itâs blown away in both blurred version, so wonât be boosted; on the other hand the two versions keep detail in different frequency ranges. So their subtraction is a way to enhance, precisely, that frequency window:
![(Fig 3.2) The subtraction between two versions of the original blurred with different radii (r1</p> <p class=]( "(Fig 3.2) The subtraction between two versions of the original blurred with different radii (r1<r2).")
(Fig 3.2) The subtraction between two versions of the original blurred with different radii (r12).
(Fig 3.3) The original plus the difference equals the sharpened version: high frequency has not been affected by DoG (to have a gentler effect it could be suggested a lower opacity LL blend or an inverse S-shaped curve to reduce the contrast of the difference layer).
(Fig 3.4) DoG with R1=4.0 and R2=20.0 and SS2, applied LL with an extra opacity lowering at 50%.
Iâm recalling here the DoG because it represent a ïŹrst step off the traditional sharpening track: I can report that itâs usually applied using a blur ratio ranging from 4:1 to 5:1, while a ratio of 1.6 mimics the Laplacian of Gaussian (LoG: an operator that calculates the second derivative of signal intensity, so itâs good for instance in ïŹnding edges. I plan to add more on LoG here later on).
I still have to test it extensively: nevertheless an important feature that should be noted is its resemblance to HiRaLoAm (as Dan Margulis uses to call USM with High Radius Low Amount). But thereâs a remarkable difference: namely, that edges are less or not sharpened at all, because they belong to the high frequency detail window thatâs untouched by DoG (less or no difference between edges in GB1 and GB2, so less or no boosting at all).This could be a beneïŹt in workïŹows where different sharpening rounds are planned and an extra step is worth its time.
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