Digital BW, The Print

>>Mathematically:  Beyond trivial response functions (i.e. an impulse
 >>function), multiple A(F)'s can produce the same outputs.  I.e. an output
 >>does *not* map to a unique input.
 >
 > It does NOT have to map to a unique input, it has to map to the same
 > response as the B&W film does, and as you should know, B&W film renders
 > different colors the same.
 >
 > This is all quite interesting, as MANY people convert RGB images to
 > grayscale, and they look quite good.  If this was so inaccurate and
 > horrible, then how DOES that work so well?

Ah, kind sir, I never asserted that one cannot get great results from the 
process.  :)  In fact, I've printed a large number of quite pleasing b&w 
prints from color originals.  However, one of your original statements,

 >I have all the information I need, the frequency and the intensity.
 >Both the color and B&W films response is deterministic to the
 >frequency and intensity...so I believe I have the information
 >necessary to map one to the other.

..is a mathematical and practical fallacy.

Simple example:

Let's say that you're using Kodak's sensor listed here:
http://members.aol.com/modernimaging/mi/Kodak_DCS-620x_Technology.htm
and Tri-X:
http://www.kodak.com/global/en/professional/support/techPubs/f9/f9.pdf 
(see page 9 for the spectral response curve)

Let's zoom in on one little cel of our test image... you have a nice blue 
object.. let's say it comes out to one very dominant at 470 nm.  Let's say 
that it's about as bright as the whole of the scene.  (We do the latter 
just so we can skip over talking about development times, over- or 
under-exposure, etc.)  Let's say that right next to it you have another 
blue object at 430 nm, same brightness.

On the CCD, these two blues excite the sensor the same amount.  They will 
both be "weighted" the same amount.  You'll get some output value B, with 
no output values R or G (their response curve is 0 at that point.. the 
argument holds even if they aren't).  Compared to the overall brightness 
of the scene, you'll get some number for B, say.. oh.. 100, for each of them.

On the Tri-X, notice that it's spectral response curve is falling through 
the blue region.  It will weight the 470 nm color less than the 430 nm 
color.  The first cel will get a brightness value (compared to the overall 
brightness of the scene) of, oh, say, 100, and the second will get a 
brightness value of, oh, say, 90.

So does RGB(0,0,100) map to B&W(90) or B&W(100)?  Ah, there's the rub... 
it maps to both, but you no longer have enough information about the input 
to be able to determine which.  Again: the mapping is not unique.

So, when you convert your RGB image to black and white to try to emulate 
Tri-X, are you going to map that triplet to 90 or 100?  Or any of the 
other numerous values it might be?

Let me state again:  it is a simple mathematical and real-world-proven 
fact that one cannot convert the output of a binning process into the 
output of another non-identical binning process in all but the most 
trivial of cases (that is, trivial response functions, such as impulse 
functions).  I see this most every week at work.

Again: this is *not* to say one can't get great b&w images by desaturating 
color images.  See my disclaimer above.  I love my trusty G2, my NPH, you 
name it.  However, one cannot claim to be able to reproduce sensor X's 
output by shaping the output curves of non-identical sensor Y, whether 
that is comparing film to film or CCD to CCD or CCD to film.  That's just 
bad science.

Peace be with you all, and signing off of this discussion to go take some 
pictures in beautiful San Diego,
-- 
Jon Dubovsky ( entropy@... )