This is a continuation of a previous post that dealt with an article in the March/April 2012 issue of photo technique entitled “Mastering the Camera Histogram for Better Exposure”. The context of the article is how to obtain the best exposure of a raw file.
In a section of the article headed “Histogram Math” Wells says the following:
An image that is mostly red (or green or blue) will have a higher number of that one color and lower numbers of the others. That is how we get the colors in our images, by mixing varying amounts of red green and blue.
Now go back to the histogram itself and remember that the left to right axis measures the spread of the tones. Then throw in the idea of the red X green X blue calculation. What that means is that because of the mathematics, only 25% of your possible tones are to the left of the midpoint of the histogram and 75% of the tones are to the right of the midpoint in that same histogram.
I have two objections to this set of statements. The first is relatively minor: in additive color spaces like RGB, you get the tri-stimulus value that defines the color by adding the amount of light in each primary rather than by multiplying them. You get the number of possible colors by multiplying the number of possible tones in each primary together, but that calculation is irrelevant for creating or using histograms.
My second objection is more significant: the percentages given are wrong. You can get to the actual numbers in two steps. The first is figuring out how many tonal values are to the right or left of the midpoint of a raw histogram. Since the sensors in cameras (both CCD and CMOS) respond linearly to light, and the midpoint of the histogram is set to the reflectance of an 18% gray card, under the assumption that the brightest object in the picture has 100% reflectance, 82% of the possible tonal values chart to the right of the center of the histogram, and 18% are to the left. The histogram uses a nonlinear horizontal axis to achieve this offset.
The only way to get 75% of the possible tonal values to the right of the center of the histogram is to postulate a system that overloads on 100% reflectance objects. Cameras are not designed that way.
If you peel back one more layer of the onion, the percent of the number possible tones to the right of the center of the histogram gets even higher. In almost all digital cameras, the histogram presented in the LCD display is derived from a JPEG image, not directly from the raw image. In most cases, the whites in the JPEG image blow out well before the whites in the raw image. The extra headroom usually amounts to a stop or two. If it’s one-stop, then 91% of the possible tonal values chart to the right of the center of the histogram and 9% are to the left. If it’s two stops, 95.5% of the possible tonal values are to the right of the center of the histogram, and 4.5% are to the left.
Note that the histogram, since it’s produced from a res’d-down version of the image, doesn’t necessarily capture all the tones in the image. This is largely an academic quibble; I’ve yet to find a situation where it caused a problem.
Note that these objections to the numbers do not negate the main thesis of the article, which is to expose to the right. Actually, they strengthen that point. I don’t think Wells had to use numbers at all to get his idea across, but, since he did, I think he has an obligation to get them right.
There is one omission that is emphasized by the lack of images of camera histograms (there are histograms presented, but they’re from image editors) is advice to look at the histogram of each of the three primaries to make sure that none is clipped. The overall, or luminance histogram, is computed from a weighted average of the red, green, and blue values, and primaries with low weighting – red and blue – can show saturation while the overall histogram looks good. This is especially true with cameras that have been modified for infrared use; on my IR cameras, the red histogram will reliably clip before the overall histogram does.
The numbers in the article give the impression that using the histogram to judge exposure is a genuinely precise business. It isn’t. You don’t know the headroom in the raw file by looking at the histogram of the camera’s JPEG conversion. There are two ameliorating factors. The low noise of today’s APS-C and larger sensors means that you can throw away some tones on the right of the histogram and still get good clean shadows. And, with all its imprecision, the histogram is a very direct tool for looking at all the tones in the image at once – it’s almost like running a spot meter over the whole scene.
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