As a result, any point on a Waveform Display has three characteristics:
1. Horizontal position, which relates directly to the horizontal position of the column of pixels being analysed
2. Vertical position, which relates to the luminance value being analysed
3. Brightness, which represents the number of pixels at that luminance which exist within that column.
Unfortunately, this is one of those things that's easier to look at than talk about.
The Waveform Monitor provides information about the luminance of the entire image, alongside at least some information as to which subjects in the image are provoking a particular luminance feature. This is achieved by using not only the two dimensions of the histogram, but by also employing brightness as a third dimension through which to impart information.
Waveform Displays at both high and low intensity allow various parts of the display to be examined in more detail
Keen observers will have noticed that a Waveform Display can potentially encounter a ranging problem similar to that suffered by a Histogram. Whereas the Histogram display can run out of vertical range when attempting to display a lot of pixels at a single luminance, a Waveform Monitor can run out of brightness range. If the output device is an 8-bit display, no more than 2 to the power of 8 (=256) levels of brightness are available. In an HD image, each horizontal position represents a column of 1080 pixels. If all 1080 of those pixels are at the same luminance, we need a brightness range on the Waveform Display of 1080 levels. In extremities, we only have a little under one-quarter the required range of 1080 pixels which could in theory be at the same brightness.
For this reason, most Waveform Monitors have a brightness or intensity adjustment which controls the amount by which the Display's intensity is increased for every pixel at a given luminance, effectively increasing or decreasing the density of the display such that a feature of interest can be clearly viewed.
A Histogram could theoretically implement a similar manually controlled vertical scaling feature to offset the problem, but I haven't seen it done.