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9. Mixed Pyramids
Strangely enough if you will, we’re allowed to mix blurring kernels and still the equations work. If you remember: 5. Combined use of different blurring kernels, I’ve found out that:
(SB - GB) = E; (Eq. 9.1)
If we modify the assumptions of the Pyramid decomposition as follows:
U0 = O; (Eq. 9.2)
U1 = SB1(O); (Eq. 9.3)
U2 = GB1(O); (Eq. 9.4)
we end up with a 2 level decomposition with:
D1 = U0 - U1 =O - SB1(O) = T; (Eq. 9.5)
Like we know from eq. 5.4.We then have:
D2 = U1 - U2 =SB1(O) - GB1(O) = E; (Eq. 9.6)
which comes from eq. 5.3. So, D1 is a frequency layer of a mixed decomposition which contains, and hence will be able to enhance,Texture alone; and D2 is a frequency layer of a mixed decomposition which contains, and hence will be able to enhance, Edges alone.
Here are the difference layers:

(Fig 9.1) O - SB1(O) = D1, the texture only detail layer (SB Radius=3,Threshold=16).

(Fig 9.2) SB1(O) - GB1(O) = D2, the edge only detail layer (GB Radius=2).
I’ll show you the full Channels and Layers palettes:

(Fig 9.3) Channels and Layers palettes of a Mixed Pyramid.
Then I’ll add the same curve adjustments layer clipped to the Dn and play with sliders. Here is an example version:
