Re: OT: 16 bit editing myth or reality?
Although I don't disagree with your conclusion, I also
recognize the same limitations as what you noted.
This is actually a class of problems for which an effective approach
already exists in statistical literature. I don't know if
there is any real statistician, probability theorist or
information theorist on this list, but I just summarize it
below. IF not interested, please skip to the next message.
Your analysis used only simple curves and not manipulations
that require multiple pixels, such as sharpening, unsharp
mask, blur, resize, etc. Therefore, without loss of
generality, you can consider a single pixel case. (The analysis
can be expanded to incorporate dependency where necessary.)
The study system can be viewed as follows:
X --> quantization1 --> manipulation --> quantization2 --> Y
Let X be a random variable with a probability distribution of
an image. Naturally, Y is another random
variable. Quantization 1 is either 8 or 16 bits. Quantization
2 is always 8 bits.
The question is how much information Y posses about X, and how
much of it is lost by applying 8-bit or 16-bit quantization in
the quantization 1. The ultimate question is what is the
difference in the two and whether it is significant in practice.
Now we can use Fisher information of Y about X as the
information measure, while quantization 1 and quantization 2
both represent communication channels wherein Shannon
information capacity is limited. This is exactly the kind of
problems tackled in the field of "information geometry"
pioneered by Shun-ichi Amari.
"I wonder how many research workers there are in various fields all
over the world, who are at this time struggling with problems whose
solutions already exist in the statistical literature." (Mark Kac 1975)
From: Yves Gauvreau <email@example.com>
Subject: OT: 16 bit editing myth or reality?
Date: Fri, 14 Dec 2007 11:39:17 -0500
> I was curious to verify that editing in 16 bit mode (16/48) was really a
> plus or a myth especially when considering a printed image.
> So I generated a large number (1 million) of normally distributed real
> numbers (doubles) in the range of [0..1]. If you made an histogram of these
> numbers it would look pretty much like what you would observe with a regular
> image. I can add that this data set is similar to a black and white image.
> I then converted these real numbers to a set of 8 bit integers [0..255] and
> also to a set of 16 bit integers [0..65535] thus creating 2 sets of values
> from the same original set of real numbers.
> I then applied 5 different curves to each set of values. The simple curve
> was y = x^1/g where x is the set of either the 8 or 16 bit integers, y is
> the resulting set of new values and g was either 1.5, 1.8, 2.0, 2.2, 2.5.
> These curves represent a mild to heavy raise of a single control point near
> input 50. All this created 5 sets of new values for both the 8 and 16 bit
> sets or 10 new sets if you prefer.
> I then counted the unique levels of the original 8 bit integer set and of 16
> bit integer set that was converted to 8 bits assuming this would happen if
> we printed our 16 bit original file.
> Next I counted the unique discrete levels present in each of the 10 data
> sets. Don't worry the software I used for this counted them for me. This
> counting would be similar to counting the bins of an histogram having a
> count of 1 or more in them. In simpler terms, I was interested to find out
> the number of levels we loose by applying a curve to an image, this would
> look like holes on an histogram.
> Here are the results:
> The 8 bit integer set as 238 out of the possible 256 levels
> curve 1 => 203 or 85.3% (203/238)
> curve 2 => 188 or 79.0%
> curve 3 => 178 or 74.8%
> curve 4 => 170 or 71.4%
> curve 5 => 159 or 66.8%
> The 16 bit integer set as also 238 out of the possible 256 levels when
> converted back to 8 bits
> curve 1 => 216 or 90.8%
> curve 2 => 203 or 85.3%
> curve 3 => 192 or 80.7%
> curve 4 => 185 or 77.7%
> curve 5 => 173 or 72.7%
> Though I started with random numbers which mean the data is not a real
> image, I took great care to use numbers that would be representative of a
> real world B&W image. Also the curve I use may not be representative of an
> actual transformation one would use on a real image but it is actually an
> inverse gamma transformation and this type of transform is used practically
> all the time in color managed environment. I think we can say that both the
> data and the curve are representative of actual editing that could be done
> on real world images though this particular data set is similar to a B&W
> image and it may not be the same with a color image.
> I think we can safely say that this particular editing simulation shows that
> we would benefit from working in 16 bit mode.
> But I remind you that other types of editing may or may not allow us to come
> to the same conclusion.
> Hope this was helpful,