I teach a class in fine art printing. During my last class we were looking at an image in Lightroom CC Classic and someone asked why the midtone spike in the image histogram exceeded the top limit. It was cut off at the top.
Since then, I have noticed this is rather common. But, I have no idea why it is or what it indicates. The response appear to be out of the graphic range of the histogram. But, so what?
It doesn't exceed the top of the histogram scale. That may appear common, only because histograms are always normalized. Data is intentionally scaled so that the peak value reaches the top (this shows low values better). And the exact count is unimportant. The range of distribution is the only thing important.
So all histograms approximately reach the full height possible (some one data value reaches the top). A histogram consisting of one spike of all pixels with only a single value will reach the top (clipping for example). Or a smooth histogram with a very wide full even range will also reach the top. However, some extreme rounding of data counts is of course necessary, because there are megapixels of values, but only a few possible pixels of histogram video display to show it. Any flat top of a peak is due to this necessary rounding.
As tonal things are adjusted, the heights may jump around, because the height does NOT represent brightness, it represents a count of pixels with that brightness, normalized to reach the top.
Let us see what the axes of the histogram represent.
I started with a simple gradient which has overall the same amount of pixels of each luminosity or brightness intensity.
Then I am adding a single zone of one gray, therefore more pixels of that particular gray are present on the image.
The gradient is the same, but as I add more gray pixels the gradient zone is smaller and smaller.
Now is obvious that the elements of the histogram are intensity (brightness or luminosity) vs amount of pixels. And this Y axis is just proportional.
The cropping of the top is for a practical reason. We normally want the histogram to tell us about some details we can not see in... well, detail.
If we wanted to know how are our bright and dark zones (red) we would need to zoom in on the vertical axis, this means you need to cap and truncate the upper zone of the graph, which is not important because this does not represent a clipping on the histogram.
We, of course, could have some logarithmic scaling, but this needs more processing power, which can not be implemented on a small camera, and it is not implemented in some applications (shame on you Ps and Lr)
But some applications, mainly video color grading ones, have a logarithmic scale called waveform.
These scales allow you to see what is happening in those areas but let you see the overall picture without the need of clipping the graph.
Some other graphs are good for other kinds of color analysis, for example, a vectorscope (Shame on you Ps and Lr)
So different graph implementations are good for some adjustments and analysis and other are good to other stuff.
A simple histogram is just a simple tool.
