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From: jbm@aurora.UUCP (Jeffrey Mulligan)
Newsgroups: comp.graphics
Subject: Re: effective resolution and anti-aliasing
Message-ID: <707@aurora.UUCP>
Date: Fri, 12-Jun-87 16:56:19 EDT
Article-I.D.: aurora.707
Posted: Fri Jun 12 16:56:19 1987
Date-Received: Sun, 21-Jun-87 00:38:03 EDT
References: <347@esunix.UUCP>
Organization: NASA Ames Research Center, Mt. View, Ca.
Lines: 72

in article <347@esunix.UUCP>, nelson@esunix.UUCP (Scott Nelson) says:
> 
> in article <1713@ames.UUCP>, lamaster@pioneer.arpa (Hugh LaMaster) says:
>> 
>> I have heard that it is possible to represent lines of less than 1 pixel in
>> width with greyscale or color images using data filtered from a higher
>> resolution image or object.
> 
> 
> Most of what I have
> seen on anti-aliasing lines is actually misleading.  The usual
> methods in the top computer graphics books have roping on the lines
> which causes moire patterns when lots of lines are together and some
> temporal aliasing effects when lines are moved slowly.
>

These types of effects will occur when the color lookup table
is not set up correctly to produce linear intensity values on
the display (gamma correction).

> 
> I have personally seen lines moving by only 1/8 of a pixel on a
> PS 390 where the motion could be seen with the unaided eye.  On
> this machine, the higher effective resolution applies to line
> positioning but not to line width.
>

On an 8-bit per pixel display, you should be able to move a line
or point by 1/500 of a pixel.  (Calculate the displacement of
the centroid of the light distribution for these two pixel pairs:
(x1,y1,i1)=(0,0,255)	(x2,y2,i2)=(1,0,254)
and
(x1,y1,i1)=(0,0,254)	(x2,y2,i2)=(1,0,255)

At a viewing distance of 3-4 feet, a pixel will typically subtend
about 1 minute of arc of visual angle.  The smallest vernier
offsets and/or motions that can be seen by the human eye are
in the range of 3-5 arc seconds; certainly never less than
1 sec. (references upon request).  To fully appreciate how small
these numbers are, consider that the foveal cones (light collecting
receptor cells) have a diameter of 30 src seconds.  The point
here is that, depending upon viewing distance, 8 bits of gray levels
may not be necessary for effective anti-aliasing.

It is interesting that anti-aliasing techiniques must necessarily
INCREASE the width of lines.

To represent lines having a width
of less than one pixel, all you can do is reduce the contrast.
Try this:  with a one-pixel-wide line on the screen, increase
your viewing distance.  The line will appear thinner until
its apparent width is equal to the optical point spread function
of the eye.  Increasing the viewing distance further will reduce the
contrast of the line but not its width.  So just make sure that
you use a viewing distance such that the pixel size is less than
or equal to 30 minutes of arc (approx. point spread diameter).

>  To get lines with an actual
> effective line width of less than one pixel you will have to buy
> a CT-6. :-)
> 

I didn't get this joke :-(




-- 

	Jeff Mulligan (jbm@ames-aurora.arpa)
	NASA/Ames Research Ctr., Mail Stop 239-3, Moffet Field CA, 94035
	(415) 694-5150