Re: Exposure function

Dave Martindale wrote:

jani.huhtanen@xxxxxxxxxxx writes:

As I suggested in my previous message, at least try plotting the
measured JPEG file response on a log-log graph.

Here is log-log and semi log for comparison:
http://www.kolumbus.fi/jahu/images/loglog_ctf.png

In log-log scale the curvature disappears from the dark end. However, the
curves do not seem to be significantly more linear than in then semilog
scale when the pixel values are in the range of 50..225. Moreover, the
slope of the linear part is constant in the semilog scale (and also in the
log-log scale), which would suggest that gamma correction is not the
correction used (or it is not the only correction used). The curves seem
to be pretty much just sifted versions of the same function.

There are a couple of important things you can see from this. First,
since the curves are now straight for the darker portion of the image,
this tells you that the camera is taking the CCD output and encoding it
directly without tone mapping. In other words, there is no "toe" in the
transfer function, where there would be one for film. The semilog graph
suggests the presence of a toe, but it's just an artifact of the
plotting method.

The second is that there are so many curves! Assuming that you
obtained the multiple curves by changing the exposure conditions
without adjusting the ISO setting of the camera, these curves show a
dramatic amount of adaptation to subject matter.
If you had done the
same experiment with film, or with the raw output of a CCD, there would
be *just one* curve of output vs. light intensity.

Perhaps you have misunderstood what I have done. There is no output vs.
light intensity, there is output vs. exposure time. Every curve corresponds
to a certain intensity or irradiance* which have exitated the given pixel.
That is, curve shifts to left when the incoming light gets more intense.
One curve corresponds to one light "beam" corresponding to one pixel with
different exposure times.

* - not sure if irradiance is the proper term for what I mean, perhaps
intensity would be better. Basicly something analogous to electron current
(perhaps photon current). That is, number of photons passing through of
unit area in unit time interval.

The effect of
changing exposure simply slides your test points left or right on the X
axis, which also slides them up or down this single curve. But every
time you change the exposure with this camera, the entire curve shifts
left or right. This tells you that the camera is automatically
adapting the overall gain of the system (the overall brightness of the
final image) to the image content, over a range that looks like
1000:1. And this must be processing done in the camera.

All I can say that the curves behave pretty much as I expected them to, but
I may be misinterpreting the results. As a single curve corresponds to as
single pixel, I don't know if one can draw conclusions that the camera
adapts to overall brightness of the image.


The third is that the curve shape does change somewhat depending on
exposure conditions. In bright conditions, there is little or no
shoulder. In dim conditions, the shoulder is very large. So the
camera isn't just adjusting overall brightness, it's also altering the
shape of the transfer function. This makes some sense, too - in
underexposed conditions, the CCD has lots of "headroom" above scene
white, so it makes sense to compress that headroom using a long
shoulder. In overexposed conditions, the CCD has no headroom - it
saturates on scene white or even before, so there's nothing to put into
a shoulder.


I partly agree with you on this. I certainly see some irradiance dependant
changes in the shape of the function. I'm not quite sure what you're
referring to as a shoulder, but I assume you mean the soft clip (i.e., the
curve approaches asymptotically 256). This is present in all cases.
However, with the few (2 to 5) left most curves (which correspond to high
intensities) seem not to follow the same shape as the others. Perhaps you
can elaborate what you meant if I misunderstood you.

I haven't noticed any adaptation in full manual mode. There might be some
additional nonlinearities when the exposure times are over 2s and cams
noise reduction kicks in.

No, see above. This camera is doing *lots* of adaptation to scene
content. It's going to be difficult to undo that processing in a
reliable way.


Perhaps, but I'm not ready to admit this just yet ;) I hope you have just
misunderstood how I did the experiment. If I'm wrong, please explain.

The CCD itself is very nearly linear; I'm sure I've seen data sheets
where the claimed gamma of the response is 0.99 or something similar (a
gamma of 1.0 would be exactly linear).

OK. Found this
http://www.asahi-net.or.jp/~rt6k-okn/ddp/digital.htm
which seems to tell the same story. Perhaps what I'm seeing is the "edge
enhancement curve" in the figure 3 or something similar?

In film, edge enhancement is a chemical effect. In digital imaging,
endge enhancement is just sharpening. I'm not sure what's going on in
the page you refer to.


That's what I thought, but I didn't really care what the guy named his
technique. The function itself was mimicin films "exposure function".

Dave

Thanks for your comments and suggestions!

--
Jani Huhtanen
Tampere University of Technology, Pori
.

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