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# 2006.09.18 01:35 "Re: alpha in Grayscale or Palette", by Graeme Gill

```Joris wrote:

> As far as I understand what you propose above, you seem not disagree
> with my statement, in fact you're looking for a suitable distance
> measure in the L*a*b* alpha space that is *not* normal eucledian
> distance.

Probably not, but does it matter ? If something like variance
cut were being used to quantize the result, computing Euclidean
distance then doesn't come into it.

But even if it did, I doubt it makes any difference. If the
4 dimension is ignored, then the effects of the alpha component
on the visual result (measured by the worst/average/etc.
effect on the resulting color against the most sensitive background)
are simply to generate sets of color aliases. A 4th dimension
should ideally then just distinguish the aliases of a given color
(ie. the pure transparency component, disconnected with any effect
it has visually), meaning that it is orthogonal, hence by definition,
it would form a Euclidean space. I'll agree though, that the raw Alpha
may not form an Euclidean dimension.

> I'm not a real world guy. Except after the theory's in place, and I do
> seem to cover some ground that way. That means, when I'm about to do
> arbitrary things, I take that as a strong hint I made a wrong turn
> somewhere. If I need to magically jump from A to B, I take that to mean
> place.

Ah well, that's the difference between us then. I'm an Engineer,
so I'm not going to get stuck trying to figure the theory out
to the n'th degree, when trying something out will take me
down the path of discovery faster. Even if trying something out
doesn't give a workable result, it might provide enough extra
information to determine what theory applies, and how.

> I'm fully aware this is not a convincing argument though. That's why I
> never used totalitarian words like 'The Wrong Thing' or such, I said
> stuff like 'seems weird'. In the end, the statement I made is that alpha
> inside palette entries (general case, not special case of one single
> transparent index) seems to smell funny and might best be avoided. Do
> you disagree?

Yes, I'm afraid I disagree. Alpha just adds another dimension. There's
no reason to think there's anything more funny about quantizing an
RGBA space, than there is about quantizing a CMYK space. The extra
redundant dimension adds some twists to understanding it, but
ultimately the visual effect can be separated from the non-visual
effect, and the scaling of the redundant dimension can be
pretty arbitrary, and still give a useful result. As an Engineer,
I'm pretty happy to deliver a useful product to a customer and
move on, rather than never attempt the solution, because I don't
have a theory to cover everything, and the experience from that
product may later bring deeper understanding.

Quantizing an RGBA space can be seen as just another space saving
measure, and could for someone's purpose, be a useful technique.
Unless someone is knocking on the door with an application that
really needs this though, I wouldn't bother with the ramifications
too much.

> > Hmm. Why would you do that ? The notional range of L* is 0 to 100,
> > and a* and b* are often taken to range from -128 to +128 (which
> > is somewhat arbitrary, but that's the nature of the colorspace
> > and the real world), so logically the Alpha should be scaled to
> > be 0 to 100 (at least as a starting point).
>
> You're putting 'logically' and 'at least as a starting point' in the
> same sentence. Don't you think there's something fishy about that?

Not in the slightest.

> You can't build a model on the basis of a particular chosen scale that
> hides the fact you're throwing in arbitrary chosen constants and expect
> to make sense. But you may indeed expect that perhaps you're getting
> more or less pleasing results. If that's the goal, fine. I'm not saying
> it shouldn't be the goal. But I do think the words 'fishy' and 'a bit
> weird' apply, and I suspect there's turns and quircks, maybe earlier on
> that road, that aren't exactly theoretically solid, and/or at least room
> for more investigation or thought.

What scale should one use for "shininess" ? What about "sharpness" ?
How about "transparency" ? What theory would guide you ?

The answer is that there is limited theory, because this isn't mathematics
or physics, these are human perceptual scales, just like color.
No theory predicts the CIE standard observer scales, they had to
be measured - ie. they are "arbitrary", because human beings
are "arbitrary".
To come up with a scale, one has to do a series of experiments
(guided by physics theory and basic logic) to try things out,
and gauge the subjective results of trying things out.

I guess since I've tackled quantizing a similar 4 dimensional space, I
have every confidence the same can be done with something like RGBA,
with a very high probability of arriving at a useful result. Yes, there
would be stuff to learn along the way, and it's a judgement call
type of statement.

> Sorry, Graeme, perhaps I'm stupid, but I can't find much disagreement,
> yet there seems to be a lot of discussion. If the core of this is due to
> my bad use of English, I appologise.

No, I think we're communicating pretty well, and I'd certainly
never pick you as a non-native speaker of English - but then
I speak "Australian" :-)

cheers,
Graeme Gill.
```