Digital BW, The Print

Not at all.  You're going through a process of thinking that I have gone
through over the last year or so.  I don't have the answers and your
questions probe exactly the gaps in my understanding but here's a start.
The CIE XYZ primary system attempts to model our human sight and XYZ_Y is
the "primary" which seeks to measure luminance IN THE WAY THE EYE SEES IT.
To quote Bruce Fraser in Real World Color Management 2nd Edition pg 41:

"...the primary Y doubles as the average luminance function of the cones -
so a color's Y value is also its luminance"

Y is a rough approximation of our logarithmic response to luminance.  The
uniform colour spaces of LAB and LUV were attempts to create colour spaces
that are perceptually uniform.  This doesn't mean they model the eye any
better but rather that "distances between points in the space predict how
different the two colours will appear to a human observer" (pg 42)  L* is
approximately the cube root of the luminance value Y.

I'm not a mathematician but I suspect that the scaling could be performed in
L*, since there is of course a relationship between L* and XYZ_Y, but if a
linear scaling of luminance in XYZ_Y is required then it's unlikely to be a
linear scaling in L*.  Roy can likely fill in the gaps as to why it's linear
in XYZ (and hence not linear in L*) and I think this is the missing piece in
your thinking (and mine).

You need to separate your thinking of linearising a printer's response and
optimal tonal mapping and compression from the image file to the dynamic
range of ink on paper.  Having very linear L* output from a printer is NOT a
satisfactory end-game because on its own it does not generate visually
pleasing renditions of images, particularly when we can't get decent blacks
(such as on matte paper).  Prints are typically "flat" and generally
"lighter than on screen". This is the very issue which drove Roy to think
about the whole topic of applying ICC methodologies to B&W printing.
Getting a B&W printer to be linear is good because it means that the printer
has a predictable response across the scale of possible values.  But we
still need a suitable formula or mechanism for mapping from our image file
space to this linear L* print space. The advantage of using an ICC profile
is that the CMM "appropriately" does the transform from any document space
to the print space.  We are no longer dependent on individual transforms for
each and every combination of workspace and print space.

As I write this I realise I do not have a full and clear understanding of
mathematics of the scaling that is done for media relative colorimetry and
Adobe black point compensation - specifically why a linear scaling in XYZ is
applicable.  I hope Roy can fill in some of the gaps.

Cheers

Steve

> From: Olivier <odesmais@...>
> Reply-To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Date: Mon, 27 Feb 2006 16:56:24 -0000
> To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Subject: Re: [Digital BW] QTR Create ICC transforms:  was Questions about
> Using Color Settings and Workspace Profiles for Grayscale Printing
> 
> The question for the perceptual intent is whether Adobe BPC and simple
>> media white point scaling are the most visually optimal methods of
> shrinking
>> the gamut to fit?  (There then exists another much more complex
> question as
>> to whether this would remain constant for "greyscales" of varying
> hue -
>> warm, cool, sepia etc.)
>> 
> 
> Well, Steve the question as I can best formulate it would be : would
> relcol simply scale L* from media white to BPCted black in a
> linearmanner (the way you linearise the printer output e.g. evenly
> spaced L* intervals) while the perceptual one would include a gamma-
> like formula to the restricted L* (L* being scaled only from media
> white to BPCted black instead of 0-100)thus preserving human
> perception and contrast.
> 
> Sorry I can't think in XYZ, and all the above probably sounds very
> naive...
> 
> 
> Olivier