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But the "B" of HSB, the "L" of HSL, and the "L" of LAB, are pretty much identical.
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B in HSB and L in HSL are kind of similiar. The formulas are rather simple and can be done with stock tools. They are kind of like step brothers or something.
L in Lab and Lum in HsY are nearly identical. If I remember correctly, you have to look into XYZ colour space (conversions) to see how nearly identical they are. Like, out to three decimal places or something.
Cheap and easy way to get Lum in HsY:
-Edit > Fill
-- Using: Black, White, or 50% Grey
-- Mode: Saturation
Another option, which is a dynamic in the Layers palette, is to fill a new layer with any shade of grey and set blending mode to Saturation.
Tada. You know have the next best thing to L in Lab without having to convert to Lab.
One of the main advantages of using Lum in HsY (or L in Lab) is that the channels are weighted. This means that yellows will be brighter and blues will be darker. If you have a photograph with lots of highly saturated hues, desaturating to L in HSL will wash-out the photograph a tad. Whereas Lum in HsY (or L in Lab) should give you more contrast to work with right off the bat.
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Apply Image and Calculations
I adore Apply Image, but I don't really use Calculations at all.
One day Mr. Cox said that Layers were meant to replace Apply Image. After thinking about that for a bit, I realized that the things that Apply Image can do can also be done in the Layers palette - but the Layers palette has the benefit of Adjustment Layers, Clipping Groups, and what-not. Think of it as tweakable Apply Image on crack. Layer ChOps as I call the techniques.
But moving things from the Channels palette to the Layers palette isn't always worth the effort. For the simple things, prolly best to stay in Channels.
For a little more finese, tweakability, and visual feed-back, take it to Layers. Can go a long way to taking out the hit-or-miss inherent in Apply Image (but I'm not sure about hit-or-miss in Calculations). Wanna adjust the choke on blues in the midtones? Layer ChOps.
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Too much on my mind regarding these things. Going to digress and hide under my rock for a bit.