Input/Output on Histograms

O.K. guys, I'm getting a handle on adjusting the left and right limits on the histograms. But I totally don't know what the upper and lower adjustments are for, i.e. input and output. Just to show my ignorance, what is input from and where is output going (I hear you laughing)? Can someone provide an explanation and/or direct me to a tutorial that covers this? DPP's tutorial is pretty lame, just telling me I can adjust these. And even though I can see what changes happen to the image as I move these bars around, I would like to actually understand the theory behind all this.
Thanks
Diane

Any image can have a range of tones that goes (if we express it in 8 bit terms) from 0 (absolute black) to 255 (absolute white). It can have that range, but it doesn't always. It might lack contrast and go from dark grey to light grey, or in other words from, say, 20 to 230. In this case you would see that the histogram doesn't fill all the box. Pulling in the sides of the box until it just fills it makes the darkest tone 0 and the lightest 255. You are now using all the possible tonal range. Put if you pull the sides in too far, shades of grey that should be close to black or white but not all the way to the extremes will be pushed too far and will be lost. This is called "clipping" and is a no-no.

Here is an explanation.

tzalman, you confirmed that I understand that part of working with the histogram, which is the input side of things. In DPP, you can also move the top and bottom lines altering the shadow and hightlight output points and thus changing the shape of the curve. That is where my understanding falls short. I will look at Peano's link and see if that clarifies things for me.
Thanks
Diane

IMO, you should not use those sliders on "real life" images. Most images have (something that approaches) pure black and white.

If you drag the black output level to 20 for instance, your deepest blacks will be 20, but you won't add anything below that...

All those sliders do is limit the maximum white or black to a lower lever than pure white or pure black as René explained. I use output limiting on rare occasion in Photoshop, but there's normally no need to ever use this in your raw converter.

I think the theory behind this is as follows :
In input you have a pixel with a given level Li (Input Level in a given channel, Red, Green or Blue doesn't matter).
The modifications you make in the histogram determine how this level Li will be transformed into a level Lo (Output Level).

For instance, when you move the vertical right bar of the histogram (white point) from 255 to 192, this means that all pixels that have a level >=192 will be transformed to 255. ok ? Now what about other pixels ? Other pixels will be transformed according to the line that goes from (0,0) to (192,255). You can easily see this line in the RGB histogram of DPP.

Now what happens if you move the upper horizontal line of the histogram ?
Well it's the same principle.
For instance if you move this line from 255 to 164, all pixels will be transformed now according to the line that goes from (0,0) to (255,164).
So there will be no pixels with a level >164 in your pic.

When you define a curve, you just replace the line by a curve.

Another way of saying it: Pulling in the sides stretches your data, pulling down the top compresses the data.

Got it tzalman - thanks!
Diane