On 12 May, Keith Packard wrote:
>
> Around 10 o'clock on May 12, [EMAIL PROTECTED] wrote:
>
>> Isn't it less misleading to say partial coverage is indistinguishable
>> from a transmissivity less than one.
>
> Or partial coverage is indistinguishable from partial opacity, which is
> more-or-less what alpha measures.
>
It is the more-or-less that is the source of some of our problems.
The following is an optical model that could be implemented in software
and that might be at least partially accelerable by present hardware. (I
wonder to what extent this is how the "gamma correction" is done in the
current hardware.)
I will start with a monochrome world and add color later. First, a
definition from the photographic imaging world:
1
Optical Density (OD) = log10 ( ------ )
(1-T)
and
T = transmissivity = fraction of light transmitted = alpha
There is no "more-or-less" here, although when encoded into integers as
required by computers there will some approximation errors.
If you perform compositing operations in OD you find that
Composite( ODi, ODj) = ODi + ODj
which is exactly what happens when I superimpose layers of transparent
material with known OD. If I superimpose four layers, with OD of
0.3, 0.3, 0.4, and 0.5 the result is an OD of 1.5. Black stencils have
an OD of Dmax. Working in OD is computationally simple and corresponds
to the photographic transparency model.
The problems with working in OD are:
1) It does not correspond the the voltages needed by CRTs. If you
are greyscale and have a spare LUT this is a minor problem. You just
put the OD -> voltage function into the LUT. If not, there must be a
computerized conversion.
2) It is a subtractive model and most computer users are accustomed to
additive models. With the OD approach, I start with a pure white image
at maximum brightness and start subtracting things. When I superimpose
a pure red and a pure green transparency I get black. In the additive
world you get yellow. Most people are accustomed to the additive
model. They can learn the difference, but existing software would also
need to be changed.
Since there is always a mapping between additive and subtractive
models this could be dealt with in the interface to the programs.
Provide both additive and subtractive interfaces, then use the
subtractive model internally.
You also want to add a kind of special stencil to provide for the
common overlay operation in additive systems. In a subtractive system
I cannot superimpose an opaque image layer. Opaque layers yield black.
But I can stencil a hole (e.g. OD of 0.0) and superimpose the image
onto the resulting white background.
The real world cannot create negative OD, but the concept of a negative
OD is mathematically well behaved and potentially very interesting as a
computer operation. It is a wierd kind of amplifying layer, perhaps
similar to a bleaching operation. This is not really needed.
3) The color model would need careful definition. In the OD world there
is no fourth alpha channel. Each pixel is defined in terms of an OD
for that color band. (I could define four color bands and get real
exotic if I wanted. I am aware of some color films that have four
color sensitive layers and get enhanced color resolution as a result.
This could be an interesting experiment for computers.)
As with 1) above, you need to convert from the color band OD into
RGB on both input and output. The output must convert OD into voltages
for the red, green, and blue guns. The input must convert from the
typical RGBA into OD. This aspect can be hidden by the interface layer.
The translation between RGBA and optical density is a matter of simple
definition, but might involve cross terms that make it more than a
simple LUT operation.
4) You need to think about resolution and range. An 8-bit resolution
for positive OD could provide an OD range of 0.0 to 2.55. This is not
too bad for the typical office PC. The actual lighting and luminance
of typical PC monitors can be mapped onto that range and look fairly
realistic. If you measure the human eye looking at film on a lightbox
or slide projector in a dimly lit room, most people can see OD
difference down to somewhere in the range of 0.001 to 0.005. (The eye
becomes rather non-linear in OD sensitivity near white and near black.
Those numbers are for tones from dark grey to light grey.) The upper
bound for usable OD range is around 3.5. The typical human eye has
problems seeing larger OD ranges. So a 12-bit encoding covers the
typical human range.
Using an 8-bit resolution opens up lots of potential with hardware
accelerators. Using a 10-, 12-, or 16-bit resolution shifts you into
the domain of computer processing, but modern vector processors can
still provide noticable acceleration for the 16-bit encodings. Some
bright soul can probably devise a 10-bit encoding that converts into
efficient 32-bit arithmetic. Compositing OD merely needs saturating
addition operations, so it can be very fast. Adding amplification
layers introduces only saturating subtraction.
R Horn
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