Color dodge eliminate yellowing. Why?

[dario]

Hi, it's me again with my comics restauration hobby.
I just discovered a nice trick to eliminate automatically the yellowing of the old pages, but i do not understand why it works. Can you explain it ?
Here is the trick
When you have a yellowed comic page (first image) create a new layer filled with the color of the paper (that supposedly was almost white at the origin).
Now invert the layer, and use Color Dodge as blending mode. The result is a restored page (second image)

I would like to understand why it works. What EXACTLY the color dodge blending mode does? I really would like to understand the math behind it (i'm good with math so don't worry )

thank Dario

[byRo]

Dario,

If that was Linear Dodge, and not Color Dodge, the formula would have been very simple. Linear Dodge is the simplest blend of all - just add the values of each channel.

In your "trick", sampling the (supposedly) white border gives a reading of around 251/241/184.
Inverting that, gives you the difference from 255 in each channel - or 004/014/071.
Adding that (if it were Linear Dodge) (not surprisingly) gets you back to 255 in each channel. The rest of the image will be brighter (because we're adding) and bluer, or less yellow (because the blue value is higher).

There is a very much simpler techique that gives the same result as the Color Dodge trick. Make a levels adjustment layer, select the White eye-dropper and click on the (supposedly) white border.
This gives exactly the same result as the Color Dodge. (and after some exploration should explain the math(s) behind it).

Rô

[mistermonday]

Dario, a good explanation by Ro.
ColorDodge brightens the backdrop color to reflect the source color. Painting with black produces no changes.
FYI, the math formula for Color Dodge is as follows:

B(cb,cs) = { Min (1, cb/(1-cs)) if cs<1
1 if cs=1

Where cb is the background color and cs is the source color
Regards,
Murray

[byRo]

Thanks Murray.

I searched (and searched) and didn't discover that! Where did you get that from? Must be interesting reading (for Geeks ).

Re-writing for (normal) channel values gets...

Min(255, b * 255/(255-a))

(adding or subtracting some 1's here and there because channel values start at 0)

By symmetry, I also got the Color Burn formula...

Max(0, 255*(1 - (255- b)/a)))

(0 for a=0)

Now I am one happy Geek!

Murray, now where did you find that?

Rô

[dario]

Originally Posted by mistermonday

B(cb,cs) = { Min (1, cb/(1-cs)) if cs<1
1 if cs=1

Thanks!
Do you have the formula for all the other blending modes too ?

Dario

[Cameraken]

Here is a link.

Look under 'Burn Modes'

http://www.pegtop.net/delphi/blendmodes/

Ken

[byRo]

Thanks Ken,

update for the link - http://www.pegtop.net/delphi/articles/blendmodes/

Seems that a bigger problem than understanding the formula is trying to describe it.......

This mode is some kind of inverted multiply mode (the multiplication is replaced by a division of the "inverse").

Rô

[Cameraken]

You are Welcome.

Here is another.

http://www.vanderlee.com/tut_fm_mixingmodes.html

Ken.

[Flora]

Hi dario!

Welcome to RP!

For all the others....

...that's really IT! .... I've had it .... I'm going to pick up knitting as a hobby!!!!

[Kraellin]

now flora, dont do that or we'd all have to take up knitting as well just to try and do as well as you do

craig

[dario]

Originally Posted by Flora

Hi dario!

Welcome to RP!

Ciao Flora, grazie

For all the others....

...that's really IT! .... I've had it .... I'm going to pick up knitting as a hobby!!!!

Am I missing something?

[Flora]

Ciao Dario!!!

Am I missing something?

.... Not really ... Fact is that I'm an absolute disaster with numbers .... and feel a bit frustrated when exposed to the knowledge of the 'numbers' geniuses we have here ...

P.S. ... probabilmente verrò condannata al rogo per questo!!!

P.P.S. ... di dove sei?

[Flora]

Craig,

....

[Ed_L]

Originally Posted by Flora

[b] I'm going to pick up knitting as a hobby!!!!

Flora, if you need help, just let me know. I quit Photoshop, and took up knitting about 6 months ago. Maybe Doug will add a knitting forum.

Dario, welcome to RP!

Ed

[Flora]

Originally Posted by Ed_L

Flora, if you need help, just let me know. I quit Photoshop, and took up knitting about 6 months ago. Maybe Doug will add a knitting forum.

... I will ask Doug about the knitting Forum .... and will be kicked out of RP at the speed of light!!!!