re:Digital vs Analog (and where to get a cheap scanner)

[P3D Gregory J. Wageman <gjw@xxxxxxxxxx>]

Peter Davis comments:

>practice of halftoning was originally done by projecting a photograph
>through a piece of glass with a finely etched grid of lines.  The
>transmission properties of that grid resulted in the halftoning effect.  The
>piece of glass had no intelligence or algorithm to accomplish it.

That's not halftoning.  I'm not sure what it is (besides possibly
just an 'effect') but it isn't halftoning.

>In signal processing terms, halftoning is really a form of "error
>dispersion."

No, it's dithering that's error dispersion.  (Digital) halftoning is
as I said, a trade-off of resolution for greyscale.  Put another way,
it is a method to get more than two apparent levels from a display
device which is physically only capable of two levels.  I'd quote you
from Foley and Van Damm's "Fundamentals of Computer Graphics", but
it's at home and I'm not.  Digital halftoning involves
using a pattern of dots to approximate a greyscale value, e.g.:

        [  ]  [x ]  [x ]  [xx]  [xx]
        [  ]  [  ]  [ x]  [ x]  [xx]
         0%    25%   50%   75%  100%

The "virtual" pixel above has 5 possible levels, but is four times
the area of the physical pixel, which has only two levels.  Dithering
(error dispersion) comes into play when you want to display a value
somewhere between these available steps (say, 30% grey in the above
example).

The difference between the desired value and the nearest representable
value (the quantization error, a signed quantity) is distributed
3/8ths to the right, 1/4th to the lower-right, and 3/8ths to the
lower neighbor pixels (before they, in turn, are quantized and have
their quantization error distributed in the same way).  This particular
form of dithering is called Floyd-Steinberg dithering.  By adjusting the
intensity of the neighbor pixels, the quantization error is averaged
out over an area, resulting in a more accurate representation than
if you simply dropped the error "on the floor".

>So, quantization alone does not make something analog or digital.

I would disagree; the characteristic of a quantity changing or being
stored in discrete steps is the fundamental property of being 'digital'.

        -Greg W.


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