Why is the mid point in PS Levels labeled as 1

[fike]

I understand that there are 256 levels of luminance in each RGB channel, and in RGB mode, that they are generally labelled as 0 to 255. I understand that there are fewer gradients on the dark end of the scale than the light end. I understand that the representation of 0-255 are integers. I understand that the levels dialog is representing a combination of all four channels, so the 0-255 construct is a bit of an artificial PS construct.

What I don't understand is why PS represents the middle point as 1.

Can anyone help me understand the wisdom of that?

[digitaldog]

I understand that there are fewer gradients on the dark end of the scale than the light end.

I don't know that's necessarily so, the encoding of the data should play a role.
The middle value is 'gamma' and thus a different value/scale than the values on either end. Again, depending on the color space, I don't think we are to take that value literally.
If the color space doesn't follow the gamma formula, (and I don't think this is the case here, at least all the time), it's probably not totally accurate to call it gamma. Not that every label in PS is technically correct. For example the Photoshop layer mode called "luminosity" is not, it is actually calculating something like the "Luma" which is an old TV RGB transform.

[fike]

But middle gray isn't represented as 1 on a scale of 0-255. It should probably be something closer to 119.

[Dave Ellis]

My take on this is that with the left and right hand sliders, you are effectively changing the black and white levels and hence there is some direct relationship to the RGB values. With the mid-point slider, you are re-distributing the mid tones but there is no direct relationship to the position of the grey point as such. The scale centered around 1.0 is just for reference purposes.

Dave

[Schewe]

The middle value is 'gamma' and thus a different value/scale than the values on either end. Again, depending on the color space, I don't think we are to take that value literally.

Andrew is correct...the middle slider in Levels is a gamma adjustment and has zero to do with 0-255 readouts. As you adjust the middle slider, the readouts are indicating an increase or decrease in the midtone levels...+1 indicates a lightening and a -1 indicates a darkening. The numeric readouts indicate the relative change in gamma.

[fdisilvestro]

The value in the middle of the levels dialogue is not the middle gray but it is related to gamma as Andrew and Jeff previously said.

To be precise, it is the inverse of gamma (1/gamma).

Once you define your minimum (black) and maximum value (white), you normalize all the values to 1, so minimum=0 and maximum=1

To obtain the output value after gamma adjustment:

    Output = input ^ (1/gamma)

The first attached image shows the effect of gamma=1, gamma=2 (1/0.5) and gamma=0.5 (1/2) 

The effect of using gamma=0.5 is the same as duplicating the visible layer and selecting blending mode "multiply"

Some people mistakenly think that changing the center value in the levels dialogue is the same as moving the middle point horizontally in the curves dialogue. This is correct only for one side of the curve, since PS changes the calculation for the other side. This is shown in the second and third figure.

The second attached image shows that when you drag the center of the curve horizontally to the right, then you get the same effect as moving the center value in the levels dialogue.

In the case of the third image, dragging the middle of the curve horizontally to the left, has a different effect, where the highlights are affected more.

The calculation in this case is:

    Output = 1 - ( 1- Input )^(1/gamma)

The fourth attached image shows the difference between the curves