Adobe After Effects CS5 : Dynamic Range: Bit Depth and Film (part 2) - Dynamic Range, Cineon Log Space

3. Dynamic Range

The pictures shown in Figure 4 were taken in sequence from a roof on a winter morning. Anyone who has ever tried to photograph a sunrise or sunset with a digital camera should immediately recognize the problem at hand, even in an era in which a phone camera can deliver HDR images. With a standard exposure, the sky comes in beautifully, but foreground houses are nearly black. Using longer exposures you can bring the houses up, but by the time they are looking good the sky is completely blown out.

Figure 4. Different exposures when recording the same scene clearly produce widely varying results.

The limiting factor here is the digital camera’s small dynamic range, which is the difference between the brightest and darkest things that can be captured in the same image. An outdoor scene has a wide array of brightnesses, but any digital device can read only a slice of them. You can change exposure to capture different ranges, but the size of the slice is fixed.

Our eyes have a much larger dynamic range and our brains have a wide array of perceptual tricks, so in real life the houses and sky are both seen easily. But even eyes have limits, such as when you try to see someone behind a bright spotlight or use a laptop computer in the sun. The spotlight has not made the person behind any darker, but when eyes adjust to bright lights (as they must to avoid injury), dark things fall out of range and simply appear black.

White on a monitor just isn’t very bright, which is one reason professionals work in dim rooms with the blinds pulled down. When you try to represent the bright sky on a dim monitor, everything else in the image has to scale down in proportion. Even when a digital camera can capture extra dynamic range, your monitor must compress it in order to display it.

Notes

Floating point decimal numbers (which are effective for storing a wide range of precise values efficiently) and high dynamic range numbers (which extend beyond monitor range) have tended to be lumped together, but each is a separate, unique concept. If your 8-bit color range is limited to 0 to 255, then as soon as you have a value of 256, or –1, you are in high dynamic range territory. Floating-point values are merely a method used to store those out-of-range values without hitting an absolute low or high cutoff.

A standard 8-bpc computer image uses values 0 to 255 to represent RGB values. If you record a value above 255—say 285 or 310—that represents a pixel beyond the monitor’s dynamic range, brighter than white or overbright. Because 8-bpc pixels can’t actually go above 255, overbright information is stored as floating-point decimals where 0.0 is black and 1.0 is white. Because floating-point numbers are virtually unbounded, 0.75, 7.5, or 750.0 are all acceptable values, even though everything above 1.0 will clip to white on the monitor (Figure 5).

Figure 11.5. Monitor white represents the upper limit for 8-bpc and 16-bpc pixels, while 32-bpc values can go arbitrarily higher (depending on format) or lower; the range also extends below absolute black, 0.0—values that are theoretical and not part of the world you see (unless you’re in outer space, staring into a black hole).

In recent years, it has become simpler to create still HDR images from a series of exposures—files that contain all light information from a scene (Figure 6). The best-known paper on the subject was published by Malik and Debevec at SIGGRAPH ’97 (www.debevec.org has details). In successive exposures, values that remain within range can be compared to describe how the camera is responding to different levels of light. That information allows a computer to connect bright areas in the scene to the darker ones and calculate accurate HDR pixel values that combine detail from each exposure.

Figure 6. Consider the floating-point pixel values for this HDR image; they relate to one another proportionally, and continue to do so whether the image is brightened or darkened, because the values do not need to clip at 1.0.

But with all the excitement surrounding HDR imaging and improvements in the dynamic range of video cameras, many forget that for decades there has been another medium available for capturing dynamic range far beyond what a computer monitor can display or a digital camera can capture.

That medium is film.

4. Cineon Log Space

A film negative gets its name because areas exposed to light ultimately become dark and opaque, and areas unexposed are made transparent during developing. Light makes dark. Hence, negative.

Dark is a relative term here. A white piece of paper makes a nice dark splotch on the negative, but a lightbulb darkens the film even more, and a photograph of the sun causes the negative to turn out darker still. By not completely exposing to even bright lights, the negative is able to capture the differences between bright highlights and really bright highlights. Film, the original image capture medium, has always been high dynamic range.

If you were to graph the increase in film “density” as increasing amounts of light expose it, you’d get something like Figure 7. In math, this is referred to as a logarithmic curve. I’ll get back to this in a moment.

Figure 7. Graph the darkening (density) of film as increasing amounts of light expose it and you get a logarithmic curve.

Digital Film

If a monitor’s maximum brightness is considered to be 1.0, the brightest value film can represent is officially considered by Kodak to be 13.53 (although using the more efficient ICC color conversion, reveals brightness values above 70). Note this only applies to a film negative that is exposed by light in the world as opposed to a film positive, which is limited by the brightness of a projector bulb, and is therefore not really considered high dynamic range. A Telecine captures the entire range of each frame and stores the frames as a sequence of 10-bit Cineon files. Those extra two bits mean that Cineon pixel values can range from 0 to 1023 instead of the 0 to 255 in 8-bit files.

Having four times as many values to work with in a Cineon file helps, but considering you have 13.53 times the range to record, care must be taken in encoding those values. The most obvious way to store all that light would simply be to evenly squeeze 0.0 to 13.53 into the 0 to 1023 range. The problem with this solution is that it would only leave 75 code values for the all-important 0.0 to 1.0 range, the same as allocated to the range 10.0 to 11.0, which you are far less interested in representing with much accuracy. Your eye can barely tell the difference between two highlights that bright—it certainly doesn’t need 75 brightness variations between them.

A proper way to encode light on film would quickly fill up the usable values with the most important 0.0 to 1.0 light and then leave space for the rest of the negative’s range. Fortunately, the film negative itself with its logarithmic response behaves just this way.

Cineon files are often said to be stored in a log color space. Actually, it is the negative that uses a log response curve and the file is simply storing the negative’s density at each pixel. In any case, the graph in Figure 8 describes how light exposes a negative and is encoded into Cineon color values according to Kodak, creator of the format.

Figure 8. Kodak’s Cineon log encoding is also expressed as a logarithmic curve, with labels for the visible black and white points that correspond to 0 and 255 in normal 8-bit pixel values.

One strange feature in this graph is that black is mapped to code value 95 instead of 0. Not only does the Cineon file store whiter-than-white (overbright) values, it also has some blacker-than-black information. This is mirrored in the film lab when a negative is printed brighter than usual and the blacker-than-black information can reveal itself. Likewise, negatives can be printed darker and take advantage of overbright detail. The standard value mapped to monitor white is 685, and everything above is considered overbright.

Close-up: All About Log

You may first have heard of logarithmic curves in high school physics class, if you ever learned about the decay of radioactive isotopes. If a radioactive material has a half-life of one year, half of it will have decayed after that time. The next year, half of what remains will decay, leaving a quarter, and so on. To calculate how much time has elapsed based on how much material remains, a logarithmic function is used. Light, another type of radiation, has a similar effect on film. At the molecular level, light causes silver halide crystals to react. If film exposed for some short period of time causes half the crystals to react, repeating the exposure will cause half of the remaining to react, and so on. This is how film gets its response curve and the ability to capture even very bright light sources. No amount of exposure can be expected to affect every single crystal.

Although the Kodak formulas are commonly used to transform log images for compositing, other methods have emerged. The idea of having light values below 0.0 is dubious at best, and many take issue with the idea that a single curve can describe all film stocks, cameras, and shooting environments. As a different approach, some visual effects facilities take care to photograph well-defined photographic charts and use the resultant film to build custom curves that differ subtly from the Kodak standard.

As much as Cineon log is a great way to encode light captured by film, it should not be used for compositing or other image transformations. This point is so important that it just has to be emphasized again:

Encoding color spaces are not compositing color spaces.

To illustrate this point, imagine you had a black pixel with Cineon value 95 next to an extremely bright pixel with Cineon’s highest code value, 1023. If these two pixels were blended together (say, if the image was being blurred), the result would be 559, which is somewhere around middle gray (0.37 to be precise). But when you consider that the extremely bright pixel has a relative brightness of 13.5, that black pixel should only have been able to bring it down to 6.75, which is still overbright white! Log space’s extra emphasis on darker values causes standard image processing operations to give those values extra weight, leading to an overall unpleasant and inaccurate darkening of the image. So, final warning: If you’re working with a log source, don’t do image processing in log space!