
A pixel is not a little square, a pixel is not a little square - ajg1977
http://www.alvyray.com/Memos/6_pixel.pdf
======
sesqu
Summary: Pixels are image samples, where the sampling methodology is
undefined. Many people assume a square area per sample, probably because it's
the easiest interpolation to make, but the author prefers point samples, which
are easiest to do math on.

The correctest interpretation depends on the sampling device, which has often
been something like gaussian for optics, and representation, which has
typically been ignored as complicated. Ironically, modern technology uses (to
my understanding) rectangular spaced subpixels in both sampling and
representation, which are still not square but much closer.

Since technologies change and pixel density is high, the point-sample
interpretation is both useful and reasonable, but I would caution against it
until we all have retina displays and 4 megapixel digital cameras.

~~~
jacobolus
> _but the author prefers point samples, which are easiest to do math on._

Easiest, and most correct, or at least a lot harder to screw up.

> _The correctest interpretation depends on the sampling device_

The “point-samples interpretation” is always perfectly correct, encompassing
other definitions. The thing that differs from one device to another is the
reconstruction filter used to interpret the meaning of those point samples.
Given that a nearest-neighbor type reconstruction filter is pretty much never
the best, using the “little square” interpretation that ties us down to that
reconstruction is counterproductive.

> _Ironically, modern technology uses rectangular spaced subpixels in both
> sampling and representation._

In sampling, I assume you mean the sensors in digital cameras? Treating them
as squares/rectangles instead of point samples is not especially useful,
because the optical system is pretty complicated, and so lens blur/chromatic
aberration/etc. are at a larger scale than the pixels themselves. Better is to
just wrap the knowledge of pixel shape and the knowledge of optical effects
into the same part of the model, the reconstruction filter.

The point-sample interpretation is perfectly relevant for current-resolution
devices. In the case of LCDs for example, you just have to keep in mind that
the sample points for R, G, and B subpixels are not the same.

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DLWormwood
I've read this before, and I sympathize with his gripes, but it strikes me as
a UX minefield to abandon the conceit now. If for no other reason, it's very
useful to see the "box filter" effect when magnifying images when doing pixel
art manipulation (still relevant for most cellphones and portable devices) as
well as examining image compression quality. If most image viewers default to
an interpolated view for magnification, I can see many graphics professionals'
jobs get worse as it becomes even harder to convince to clients provide vector
image files or raster images of sufficiently high resolution, since end users
wouldn't see such an obvious distinction anymore.

~~~
jacobolus
The “box filter effect” is only really helpful to someone who understands that
the appearance of the magnified boxes is not remotely like the appearance of
the final image. Its main utility is showing pixel artist that the samples are
_discrete_ , and very explicitly indicating their spacing.

I don’t agree with you that the upsized box UI is necessarily the most
intuitive or useful, but instead is just the only UI that has really been
tested. I can imagine several other possibilities, for example showing a
smooth interpolation (indicating something closer to real-world appearance)
overlaid by a circle at each sample center (indicating color of the discrete
sample). [That's an idea off the top of my head; I don't know if it would work
in practice.]

------
Robin_Message
Also, isn't he missing LCDs, where you really do have little squares of colour
(albeit with borders)? Or is that the point? In fact, what is the point? All I
got was rant and sampling theorems.

~~~
astrange
LCD pixels are a set of three monochrome rectangles placed next to each other
horizontally. Except for the ones that are vertical. And PenTile, which is
missing some subpixels. And TVs, which display anamorphic video (or might be
768p) and whose pixels are not mapped to the monitor pixels.

None of them are little squares of one color.

What's wrong with sampling theorems anyway?

------
bbulkow
This is a _15 year old_ paper. Alvy Ray is a great guy, a luminary, love the
paper, but at this point it's a historical document.

The basic discussion was covered in my college graphics class in _1988_.
Anyone working in graphics, fonts, rendering or gaming who thinks this is news
should have their literature examined.

------
jacobolus
For more on pixels, a talk and a paper by Dick Lyon:

[http://video.google.com/videoplay?docid=-5655850487750051532...](http://video.google.com/videoplay?docid=-5655850487750051532#)

[http://www.dicklyon.com/tech/Photography/Pixel-
SPIE06-Lyon.p...](http://www.dicklyon.com/tech/Photography/Pixel-
SPIE06-Lyon.pdf)

------
davi
This came up recently in the Fiji project (a distribution of ImageJ and
associated plugins):

[http://groups.google.com/group/fiji-
devel/browse_thread/thre...](http://groups.google.com/group/fiji-
devel/browse_thread/thread/01d7aa64a7df2145/6d3ccd8cb3894d15?#6d3ccd8cb3894d15)

------
tjmaxal
This is from 1995, is this still relevant?

~~~
mattmillr
The "until we all have retina displays and 4 megapixel digital cameras." from
sesqu's summary is what makes it still relevant. Or newly relevant?

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rryan
Am I the only one who was horrified by the typesetting of that document? It
made it impossible to read.

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CamperBob
Unless I'm missing something (likely given the author's reputation), he goes
off the rails on the very first page when he defines a pixel's coverage as
[0,1] and not [0,1). Fill-convention discipline is at least as important as
sampling considerations.

~~~
jacobolus
We’re talking about samples of a (might-as-well-be) continuous space. Whether
the interval is open or closed is irrelevant. If you want to think of that as
an open paren, go ahead; the rest doesn’t depend on that at all.

~~~
CamperBob
It's irrelevant until you start applying rasterops to those pixels and areas.

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silly2
this one dies at the mention that stoch screening for print is new. yeah, in
the eighties boys. ooh, he didn't call it that. or mention any relevant color
model

all the rest is similar shick horror of anyone who never paid any atenntion to
anything.

~~~
silly2
sorry, credit must be given to an actual pdf of >4k words trying to look
serious with awful, really unreadable. typography.

yup, that's how i learned to con, mod me down etc, but believe it.

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silly2
god of mercy, can someone link to the old ttf hinting pages on msft opentype
stuff?

got author nailed there, promise you

