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Old 11/13/06, 09:49 PM   #7 (permalink)
markedavison
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Join Date: 10/08/05
Posts: 23
Default Re: Speculating on why profiling works: impossible colors?

The M8 is not a mysterious device. You can think of its color response as a machine which takes in a spectral power distribution (SPD) from a small portion of the scene (this is a function of wavelength that tells you the amount of power at each wavelength), and then produces device R, G, and B values. Each of these values is obtained by multiplying the incoming spectral power distribution by the spectral sensitivity of the corresponding channel, and then summing over all the frequencies for which the channel has a non-zero response. (Followed by scaling by a constant.) The resulting R, G, B values are the linear device R, G, B.

There is a central intuition here: cameras do not photograph colors, they photograph spectral power distributions. Two objects which appear to have the same color to the human eye may have different SPDs and yield different R, G, B outputs from the camera.

If two different spectral power distributions get mapped into the same R,G, and B values, there is no way to tell them apart by looking at the camera output. These two SPDs are said to be metameric pairs for the device.

A camera profile is a mathematical description of a function which takes a device R, G, B triple and maps it into a color space which describes human color response, such as CIE X,Y,Z space. (Note that CIE X,Y,Z space describes human color response by three particular spectral sensitivity functions, xbar, ybar and zbar.)

There are roughly two types of profiles.

The first type is a generic profile, intended for unrestricted use. You can show that it cannot be made to be accurate for all possible SPDs, unless each of the spectral sensitivity curves of the camera is an exact linear combination of the CIE spectral sensitivity functions. At best the results will be pleasing, but they will not be accurate for all input SPDs. (Technical note: if you examine a camera profile with a profile inspector you will discover that the look up table for the mapping contains output values for every possible combination of device R, G, and B. However, you can show mathematically that as the input SPD ranges over all possible spectra, the camera R, G, B triples lie inside a restricted gamut. Some of the LUT output values may indeed lie in the "impossible colors" of CIE X, Y, Z space, but this doesn't tell you if the range of values which would come from realizable device R, G, B triples ever hits an impossible color. Also, examining the range of the LUT output values doesn't tell you anything about the IR sensitivity of the camera--you need to see the spectral sensitivity curves of the camera.)

The second type of profile is intended for use on a restricted set of SPDs. For instance, if you are using the digital camera to copy color photographic prints of a given type, then the space of possible input SPDs is restricted to those which appear in the prints. Since there are only three dyes in the prints, this is going to be a much smaller space than the space of all possible SPDs seen in the world. If you profile a digital camera using an IT8 photographic target, this is the type of profile you are creating. A somewhat larger set of SPDs will be encountered if you use a color checker chart.

It is quite possible to correct IR casts by profiling if you are only using SPDs from a restricted space, there are no two SPDs in the profile test set which yield the same device R, G, B values, you only photograph scenes which are well represented by the set of test SPDs, and the spectral power distribution of the illuminating light is the same as the light used to create the profile.

Note: if you look at linear device R, G, B values it is straightforward to understand the effects of device sensitivity curves which are non-zero in the infra-red wavelengths. Suppose that we could find two filters, one which transmitted visible wavelengths perfectly, but blocked all IR, and another which did the reverse. Take a spectral power disrbution S. Then the camera response for S is simply the sum of the responses with the visual pass filter and the IR pass filter:

(R, G, B) = (Rvis, Gvis, Bvis) + (Rir, Gir, Bir).

I have been taking some pictures through the M8 with an infrared pass filer (a HOYA R72) and the results are quite interesting. You can see that under incandescent illumination, which is rich in infrared, a piece of black anodized aluminum (like a black Leica M lens) has a very sizable infrared response, which is high in red and blue. In the visible wavelengths, the piece is quite dark, and appears black, with no hue. Therefore the infrared contribution to the sum is big enough to push the hue to magenta.

The effect, however, is not limited to black synthetic fabrics and anodized aluminum. Under incandescent illumination even something as organic as an apple has a visible infrared response with the M8. It is small, but enough to change the hue just a little bit.

Rephotographing the apple with an IR cut filter (I used a Tiffen Standard Hot Mirror), produces a visible change in the hues of the apple, and gives them a much more natural appearance.

Skin tones of fair skinned people also show similar small but quite visible shifts.

The IR sensitivity of the M8 is not unique in the world of digital cameras. I have a Nikon D2h which displays similar IR responses.

There is a general misunderstanding among digital photographers that physical photographic filters are not necessary with digital because all filtration can be done after the fact. But that is simply not true, as the case of extended IR sensitivity proves.

The straightforward conclusion is: if you have an IR sensitive digital camera, and you want to create natural looking color photographs of the world without restricting the types of objects or the illumination, buy a good IR cut filter.
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