Levels and Linearity

P
Posted By
Phosphor
Jun 28, 2003
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630
Replies
10
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Closed
Lawrence,

"…For instance, Black is off by 15, so I set the end point to 13 and then move the Gamma slider to 1.13."

I assume you set the shadows slider at 13 believing that stopping just short of 15 was the conservative thing to do. But out of what hat did you pull the 1.13 gamma correction? Or was that the reading of the gamma slider after you eyeballed the image for best-looking result?

George

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LH
Lawrence Hudetz
Jun 28, 2003
Actually, that’s true. I arrived at correcting the gamma slider by adding xx from the Black slider to 1.0 on the gamma, giving Black: xx, Gamma,1.xx and no change to White. If I change both Black and White, I move the gamma to restore middle gray. It may mean that the gamma will move <1.00. I have done this eyeballing, but discovered that I could put some numbers on it.

This is all empirical, of course!
P
Phosphor
Jun 28, 2003
Lawrence,

The three input level boxes in the Levels dialog box were not created equal.

Entries in the two end boxes correspond linearly to their slider positions. The middle box entry, however, is not so related to the mid-tone slider.

The middle box entry is the reciprocal of the power to which the input is raised to correct the output on a power curve applied to a fraction (ends anchored at 0 and 1). You should not look for any particular relationship or correspondence between these sliders. To expect that 1.xx should be entered in the midtones box if xx is added to the shadows box is (please, no offense intended) nonsense.

George
LH
Lawrence Hudetz
Jun 28, 2003
Thank you, George,

Of course, a 1:1 correspondence is nonsense. I understand power functions. At some point however, a correspondence at an acceptable level is possible, for, if you note, I did arrive at this possibility empirically. The correspondence works for slider compensations up to about 15 on the Black end. This is established visually, as I have stated. You can, if you so desire, reset a specific midtone back to it’s starting value. Beyond about 15, it falls apart. I then generally go to curves to establish the "look" I want.

The middle box entry is the reciprocal of the power to which the input is raised to correct the output on a power curve applied to a fraction (ends anchored at 0 and 1).

A fraction of what?
I can establish a relationship by doing a long series of measurements, aided by knowledge of the specific values for the power law equation, as well as the equation itself. I posted this to see what, if anything, has been done by others in this regard. If anyone else wishes to weigh in on this, it would be appreciated.
P
Phosphor
Jun 28, 2003
Lawrence,

As you and I have discussed in other threads, the fraction to which the power is applied is the color value (in a given channel) divided by 255.

More polished treatments of color values "normalize" the range so that 0-255 becomes 0-1.

That the base of the gamma function is a fraction is most important in that, for fractions, the higher the power the lower the result—just the opposite for bases greater than 1.

George
LH
Lawrence Hudetz
Jun 28, 2003
As I recall ( hard tonite, See "Friday Nite Libations in the Lounge!) We were discussing the Gamma settings differences. That is a fixed value; in this case the value is adjustable, and I would expect some pretty dramatic curves changes if we plotted the input/output parameters at given settngs. Moving the end points streches the data over a wider range, which distorts the values, so moving the middle slider readjusts the relationships between those values to the right of the set point and those to the left. I was musing over the settings that could establish (or re-establish) a linear input/output relationship.

Anyway, Mule’s kicking in!
P
Phosphor
Jun 28, 2003
Lawrence,

Moving the shadows slider does not alter input/output linearity. There is no need to make a countermove for the purpose of restoring linearity not lost.

The preservation of linearity is best seen by looking at the Curves chart as you drag the left anchor rightward—the curve remains a straight line.

While darkening all points (except values of 255), rightward movement of the shadows slider increases CONTRAST from the tone to which the slider is moved all the way upward. The contrast improvement occurs becuse the darkening tapers off as tonal value increases.

Tones to the left of the shadows slider are, of course, blacked out but, if there are no such input tones to begin with, no detail is lost. You gain detail where you need it without the penalty of losing detail elsewhere provided you stop the slider at the tonal threshold for the image being edited.

The middle slider DOES introduce input/output non-linearity. There are a number of reasons for wanting to do so, not the least of which is to counteract (correct) an undesirable system non-linear effect. That’s why the slider is seen as a "gamma correction" tool.

Lawrence, I realize you know this stuff and would have no argument with anything beyond the first paragraph. At the risk of pedantry, I belabor some of it for the benefit of interested lurkers—or perhaps we are just talking to ourselves. 🙂 !!

George
LH
Lawrence Hudetz
Jun 28, 2003
Thanks again George. A good point about using the Curves anchor point as an example. I must assume then, that moving the Black slider in Levels is tantamount to moving the Anchor point in Curves. I was not sure that was so, hence the posting. That being so, moving the Gamma slider definitely creates non-linearity!

The point of all this is because I am trying for a complete calibration of the system. My goal is simple. The output matches the input, within some tolerance (which seems to have no spec). So far, I have a cal’ed monitor, a profiled printer, but my scanner is as supplied by Epson. So, I used the Q-13 charts From Kosak as a starting point and found that the neutrality was quite good,+/- 1 point on the scale of 256, in RGB. (Haven’t looked in Lab yet) So, I printed the scan unadjusted (except for the printer profile and a curves tweak noted below)and it didn’t match the original. Too red. I rescanned the printed piece read off the color shifts and brought it back to neutrality,+/- about 2 points. I opened the original scan of the Kodak step tablet, applied correction, reprinted it and now the new print overshoots: it looks (and measures) too green. To me, non-linearity became a question. Why? Because if I print a step tablet generated in Photoshop, print through the profile generated for the machine paper combo, and with a slight tweak in curves I can get a near perfect grayscale from black to white. So, If the scanner is producing a flat output, where did the color shift occur?

Edit: As I read this, I realize that, while things are "pretty good" they are not perfect, and I am suspecting a buildup of tolerance errors. Also, I haven’t calibrated the step tablet, and it may well be not as flat as indicated.
P
Phosphor
Jun 29, 2003
"…I must assume then, that moving the Black slider in Levels is tantamount to moving the Anchor point in Curves…"

Yes, and to elaborate a bit…

Sliding the Curves anchor points up or down vertically (climbing the walls) is exactly equivalent to moving one or the other of the two Levels OUTPUT sliders left or right.

Sliding the Curves anchor points left or right horizontally (along the floor or ceiling) is exactly equivalent to moving one or the other of the two END (as distinguished from middle) Levels INPUT sliders left or right

George
LH
Lawrence Hudetz
Jun 29, 2003
Gotcha!
Thanks……..
P
Phosphor
Jun 29, 2003
Lawrence,

Sorry to have addressed your question only peripherally. In doing so, I think I have obscured the main thrust of your problem/objective as re-stated in your reply #8. It’s really a color management issue beyond my ken. Why don’t you restate it in another thread which I promise not to contaminate with distractions from the central theme.

George

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