## 1204: "Detail"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

San Fran Sam
Posts: 228
Joined: Tue Nov 15, 2011 5:54 pm UTC

### Re: 1204: "Detail"

chaosmage wrote:My life is complete, I found a typo on xkcd.

There's an I missing in "NEGHBORHOOD".

See that's the joke. He knew some people would get so hung up on the neighborhood-neighbourhood thing that no one would notice the missing "I".

Well played, sir, well played.

Davidy
Posts: 221
Joined: Sat Dec 01, 2012 1:18 am UTC

### Re: 1204: "Detail"

Sebastiaan wrote:
taemyr wrote:
Sebastiaan wrote:
ijuin wrote:Even if the earth was a completely random mess of particles, the sheer amount of particles makes it very likely that there are (pseudo-)patterns of particles that can be mapped exactly with less bits than the amount of particles represented.

No lossless compresion algorithm can achieve a average compression ratio better than 1.0 on random data.

Point taken, you're absolutely right, the counting argument. The thing is that we do not have to store any possible, random configuration of earth's particles, we might just start with one. Chances are* that there is an algorithm that can store that piece of information in less bits that piece itself amounts. This algorithm might be useless on another random configuration of Earth's particles, as on average no algorithm can achieve a compression ratio better than 1.0, but for a single configuration or a subset of configurations, you might find a more effective algorithm.

*) Indeed, chances are, not "there is a always a function that...".

Someone should contact Stephen Wright. He has a head start with his map of the United States with a 1:1 scale.
"It's only funny until someone loses an eye, then it's still funny but they can only see it in 2-D."

Technical Ben
Posts: 2986
Joined: Tue May 27, 2008 10:42 pm UTC

### Re: 1204: "Detail"

DeGuerre wrote:
Pfhorrest wrote:It's basically "how far can you zoom". A resolution of one meter would mean everything within a given 1m square on the ground would show up as just a block of a single color, i.e. one pixel.

Repeat after me:

A pixel is not a little square.
A pixel is not a little square.
A pixel is not a little square.

(For those who don't get the reference.)

It is if I'm referencing the "squares*" of displayed colours on my screen. In fact, I hate having to work with pixels that are not square.

thevicente wrote:
Antior wrote:The Planck length is the limit at which physics as we know them stop making sense.

Measuring, in the practical sense means hitting stuff with other stuff

Anyway, to get smaller than the atom/electron level is very difficult.

Oh, hey i didn't see you guys all the way over there. http://xkcd.com/435/

Yep, you guys get to measure infinitesimally small things! http://www.youtube.com/watch?v=u7Z9UnWO ... p3uz647V5A

*close enough by assumption
It's all physics and stamp collecting.
It's not a particle or a wave. It's just an exchange.

hamjudo
Posts: 108
Joined: Wed Feb 16, 2011 6:56 pm UTC

### Re: 1204: "Detail"

My son was born August 23 1995. I used internet math to calculate that my son would weigh 897 pounds on his first birthday. This was the period when Worldcom's financial models assumed that the percentage of Americans with internet service would continue doubling for years into the future. I figured if the financial wizards at Worldcom felt safe in extrapolating past the point when 400% of Americans had dialup modems, that math had to be good enough for babies.

Turns out that we were both wrong. Worldcom failed spectacularly even before 100% of Americans got dialup. My son is 17 and only weighs 130 pounds.

creaothceann
Posts: 34
Joined: Fri Jan 26, 2007 9:44 am UTC
Location: Germany

### Re: 1204: "Detail"

sep332 wrote:
andyfrommk wrote:
time burglar wrote:
andyfrommk wrote:Anybody else spotted that he misspelled neighborhood?

Yes, he forgot the u

It is some sort of profound joke - he's saying "there's no u or i in neighbourhood"?

Being British, I almost spelt it that way.
I think there hidden depth in every XKCD comic that I don't get

I think you mean "spelled"

The Plank length is just one of the Plank units https://en.wikipedia.org/wiki/Planck_units which are derived from universal constants instead of "how big is the king's foot" or "how far is it from the equator to the pole" kind of units.

...

ctdonath
Posts: 198
Joined: Wed Feb 08, 2012 2:40 pm UTC

### Re: 1204: "Detail"

hamjudo wrote:Worldcom's financial models assumed that the percentage of Americans with internet service would continue doubling for years into the future.

Seems they were right, except the increase folded into increased per-user bandwidth instead of increased per-bandwidth users. Total bits delivered was the correct prediction, they just couldn't conceive of a dozen T1 lines per user...wireless...to a then-awesome Cray 2 supercomputer smaller than a deck of cards - now that was just an insane prediction to make, so the closest thing to a sensible prediction was continued doubling of users.

lgw
Posts: 437
Joined: Mon Apr 12, 2010 10:52 pm UTC

### Re: 1204: "Detail"

webdude wrote:Next time I need to ascertain the mass of a log, I'll be sure to use a log scale.
------------

Years ago I saw a box - a large crate, actually, a bit bigger than a large refrigerator/freezer. It was on a wheeled platform, and was being VERY slowly and carefully guided down the rather steep sidewalk towards one of the biology buildings. The number of men clustered around the crate seemed excessive - so many that some could not fit in to handle the crate, but were walking along, keeping an eye on the move. The men were so intent on their work I didn't want to interrupt them. I asked my brother, a Plant Sciences T.A., what was going on. He said, "oh, it's the new scanning electron microscope."

I asked why so they were using so many guys. My brother replied, "they dropped the first one; that's the replacement."

This was back in the days when you could easily buy three or four nice houses for the price of one SEM. Ouch!

Well, it could have been worse! "Hey, who unbolted the mounting plate?"

I think the only guys who can claim to have had a worse day at work than accidentally doing \$135M damage to a satellite are the pilots of that B2 that crashed on takeoff.
"In no set of physics laws do you get two cats." - doogly

lgw
Posts: 437
Joined: Mon Apr 12, 2010 10:52 pm UTC

### Re: 1204: "Detail"

Kit. wrote:
DeGuerre wrote:
Pfhorrest wrote:It's basically "how far can you zoom". A resolution of one meter would mean everything within a given 1m square on the ground would show up as just a block of a single color, i.e. one pixel.

Repeat after me:

A pixel is not a little square.
A pixel is not a little square.
A pixel is not a little square.

(For those who don't get the reference.)

Microsoft at its... well, not exactly worst, but you got the idea.

A pixel is a little square (rectangle, actually, but anyway). If you want to describe images in something that is not little squares, go find your own word.

When that was written, a pixel was three lights, each a different color, somewhat near one another. But regardless, "a little square" is a terrible way to think of a pixel in a stored image format. A pixel is a sample of the image centered at a point. The worst way to sample is to divide the image into cells and then represent each cell as a number - that forces aliasing into the stored image. A better way to sample is to take a weighted average of the image near each point - weighting close more than far. Taken to the extreme you get a holographic format, where every pixel was a sample of the whole image, but ideal for image reproduction lies somewhere in between.

A great image format does not require anti-aliasing by the display, makes sub-pixel rendering easy, and still looks good if the pixel count on the display and the image don't match well.

EDIT: Better still you don't sample the image on a grid, you sample more frequently where the image is interesting, and less where it's not.

Come to think of it, all of that is a good metaphor for quantum uncertainty. A little ball or point is a bad way to think of an electron. A model where we divide the universe into a small-scale grid where for each cell we represent the electron field by the chance of an electron in that box is more accurate, but not very helpful. A model where we choose to sample at local maximas in the electron field, calling those the "locations" of the electrons is a useful and accurate model (with a footnote about the field distribution near our sample, for when that degree of detail matters).
Last edited by lgw on Fri Apr 26, 2013 6:51 pm UTC, edited 2 times in total.
"In no set of physics laws do you get two cats." - doogly

da Doctah
Posts: 976
Joined: Fri Feb 03, 2012 6:27 am UTC

### Re: 1204: "Detail"

Davidy wrote:Someone should contact Stephen Wright. He has a head start with his map of the United States with a 1:1 scale.

Which he stole from Lewis Carroll.

…from Sylvie and Bruno Concluded, by Lewis Carroll, 1893…

‘That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

“About six inches to the mile.”

“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”

“Have you used it much?” I enquired.

“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

brenok
Needs Directions
Posts: 507
Joined: Mon Oct 17, 2011 5:35 pm UTC
Location: Brazil

### Re: 1204: "Detail"

creaothceann wrote:...

What exactly does that means?

lgw wrote:I think the only guys who can claim to have had a worse day at work than accidentally doing \$135M damage to a satellite are the pilots of that B2 that crashed on takeoff.

The Costa Concordia captain would come close...

Ray Kremer
Posts: 46
Joined: Fri Apr 26, 2013 8:21 pm UTC

### Re: 1204: "Detail"

Running an SEM off a google map car would be tricky, you'd need a pre-map car to coat everything non-metallic in carbon or gold or something.

Also, comic # 1162.

Fire Brns
Posts: 1114
Joined: Thu Oct 20, 2011 2:25 pm UTC

### Re: 1204: "Detail"

lgw wrote:Well, it could have been worse! "Hey, who unbolted the mounting plate?"

The satellite wasn't a complete loss, Lockheed Martin agreed to cover around 30 million in repair expenses. Not even a quarter of the cost of the satellite itself.

Edit because I meant to type this and got sidetracked:

brenok wrote:
creaothceann wrote:...

What exactly does that means?
It is in reply to a post that corrected another person's spelling(spelt and spelled) and then mucked up "Planck" with "plank".
Pfhorrest wrote:As someone who is not easily offended, I don't really mind anything in this conversation.
Mighty Jalapeno wrote:It was the Renaissance. Everyone was Italian.

brenok
Needs Directions
Posts: 507
Joined: Mon Oct 17, 2011 5:35 pm UTC
Location: Brazil

### Re: 1204: "Detail"

Fire Brns wrote:
brenok wrote:
creaothceann wrote:...

What exactly does that means?
It is in reply to a post that corrected another person's spelling(spelt and spelled) and then mucked up "Planck" with "plank".

Due to the " " I thought he was joking, at least on the correction, as both are accepted spellings.

Fire Brns
Posts: 1114
Joined: Thu Oct 20, 2011 2:25 pm UTC

### Re: 1204: "Detail"

the "plank" part was still the focus of it. It was wrong regardless.
Pfhorrest wrote:As someone who is not easily offended, I don't really mind anything in this conversation.
Mighty Jalapeno wrote:It was the Renaissance. Everyone was Italian.

webdude
Posts: 57
Joined: Tue Feb 15, 2011 6:11 am UTC

### Re: 1204: "Detail"

Fire Brns wrote:
lgw wrote:Well, it could have been worse! "Hey, who unbolted the mounting plate?"

The satellite wasn't a complete loss, Lockheed Martin agreed to cover around 30 million in repair expenses. Not even a quarter of the cost of the satellite itself.

Igw: Thanks for the reminder about that "mishap." Which leads me to wonder at what point damages are due to "mishaps" rather than to "total f---ups" or related phrases?

Re the B2: The pilots were not faulted; the crash was attributed to water intrusion into the avionics and the ground crew's failure to notice the problem, leading to computer navigation errors. When the media discuss "worst weather disasters" in terms of cost, they ignore the \$1.4 billion B2 loss, which was weather-related.

Fire Brns: The repair was more expensive, because Lockheed also forfeited over \$120m in projected profit. Of course, that pales in comparison to the MCO "mishap." What kind of moronic managers use the English measurement system, then ignore at least two navigators who notice the problem?

Don't worry - I heard all the managers involved were terminated, and found new employment in the housing financing industry.

squonk
Posts: 131
Joined: Fri May 21, 2010 12:25 pm UTC

### Re: 1204: "Detail"

When the lines converge, we'll be ready to send out the probe that will one day find Captain Picard and have him experience what our way of life was like.

willpellmn
Posts: 93
Joined: Wed Apr 21, 2010 11:05 am UTC

### Re: 1204: "Detail"

I'm not familiar with Google Earth per se, but it's essentially a twin to Google Maps, which I absolutely love. "Walking" around town with Street view, either in my home city or in one I'll probably never visit, is just a magnificent way to kill a half-hour or so and marvel at the rich variety of our world.

arthurd006_5
Posts: 98
Joined: Mon Oct 18, 2010 9:49 am UTC

### Re: 1204: "Detail"

J L wrote:
Jean Baudrillard wrote:When the map covers the whole territory, something like the principle of reality disappears.

Brace yourselves, the age of simulacra is coming ...

My mother has been walking around Christchurch-before-the-earthquakes in street view, and only sort-of knows that the material world is now quite different.

arthurd006_5
Posts: 98
Joined: Mon Oct 18, 2010 9:49 am UTC

### Re: 1204: "Detail"

Sebastiaan wrote:Chances are* that there is an algorithm that can store that piece of information in less bits that piece itself amounts. This algorithm might be useless on another random configuration of Earth's particles, as on average no algorithm can achieve a compression ratio better than 1.0, but for a single configuration or a subset of configurations, you might find a more effective algorithm.

*) Indeed, chances are, not "there is a always a function that...".

This is Kolmogorov complexity: https://en.wikipedia.org/wiki/Kolmogorov_complexity

I vaguely suspect that even in this regime, there is a significant proportion of incompressible strings.

Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

### Re: 1204: "Detail"

da Doctah wrote:
Davidy wrote:Someone should contact Stephen Wright. He has a head start with his map of the United States with a 1:1 scale.

Which he stole from Lewis Carroll.

…from Sylvie and Bruno Concluded, by Lewis Carroll, 1893…

‘That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

“About six inches to the mile.”

“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”

“Have you used it much?” I enquired.

“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

They are clearly not taking it far enough. A 1:1 map isn't any better than reality, but how about making a map twice as big as the world?

Edit: Also, Google Earth on a sufficiently large monitor is a 1:1 map. Cool!

da Doctah
Posts: 976
Joined: Fri Feb 03, 2012 6:27 am UTC

### Re: 1204: "Detail"

Using the country itself as its own map (and noticing that it does only "nearly" as well) hides a philosophical point about why we make maps instead of just schlepping around a bunch of satellite pics. A map simplifies the terrain it depicts, omitting or minimizing some features while emphasizing others.

Think of the difference between a Michelin road map of the Iberian peninsula, with all the roads, hills and tourist-attraction buildings shown but precious little detail about the surrounding seas, and a nautical chart of the same region where everything on land is reduced to a mere tracing of the shoreline but the water is full of all sorts of symbols significant to the sailors who use it.

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

### Re: 1204: "Detail"

lgw wrote:
Kit. wrote:
DeGuerre wrote:
Pfhorrest wrote:It's basically "how far can you zoom". A resolution of one meter would mean everything within a given 1m square on the ground would show up as just a block of a single color, i.e. one pixel.

Repeat after me:

A pixel is not a little square.
A pixel is not a little square.
A pixel is not a little square.

(For those who don't get the reference.)

Microsoft at its... well, not exactly worst, but you got the idea.

A pixel is a little square (rectangle, actually, but anyway). If you want to describe images in something that is not little squares, go find your own word.

When that was written, a pixel was three lights, each a different color, somewhat near one another.

A pixel has never been "three lights".

When that was written, I was working with pixels that were unweighted grayscale averages over cells in a rectangular grid. They had been basically this way since the word "pixel" was introduced.

lgw wrote:But regardless, "a little square" is a terrible way to think of a pixel in a stored image format. A pixel is a sample of the image centered at a point.

Nope, a pixel in an digitized image is not a point sample. It's an average over area, and the area may not even have a single point represented by the resulting value (usual for images innately monochrome on micro-level, like images acquired from silver photo film or fingerprint images or re-scanned images of dithered single-ink prints).

lgw wrote:The worst way to sample is to divide the image into cells and then represent each cell as a number - that forces aliasing into the stored image.

Then you should probably tell all the imaging sensors manufacturers around the world that they are doing it wrong.

J L
Posts: 242
Joined: Mon Jan 25, 2010 11:03 am UTC
Location: Germany
Contact:

### Re: 1204: "Detail"

arthurd006_5 wrote:
J L wrote:
Jean Baudrillard wrote:When the map covers the whole territory, something like the principle of reality disappears.

Brace yourselves, the age of simulacra is coming ...

My mother has been walking around Christchurch-before-the-earthquakes in street view, and only sort-of knows that the material world is now quite different.

Friends of mine recently started to give me directions by means of Ingress portal locations.

mrob27
Posts: 1330
Joined: Tue Jun 28, 2011 2:19 am UTC
Location: ]〖
Contact:

### Re: 1204: "Detail"

This doesn't seem to have been mentioned, but:

if the prediction works, the electron microscope alt text will be relevant by around 2036...
Robert Munafohttp://mrob.com@mrob_27

I ᴍᴀᴅᴇ sᴏɍᴛᴡᴀʀᴇ ᴛʜᴀᴛ Rᴀɴᴅᴀʟʟ ɍᴏᴜɴᴅ ᴜsᴇɍᴜʟ ɪɴ ᴛʜɪs хᴋᴄᴅ

DeGuerre
Posts: 51
Joined: Mon Feb 04, 2008 6:41 am UTC

### Re: 1204: "Detail"

Kit. wrote:Microsoft at its... well, not exactly worst, but you got the idea.

Actually, Alvy Ray Smith wrote the first version of that memo when he was working at Pixar. You might want to rethink your company prejudice.

DeGuerre
Posts: 51
Joined: Mon Feb 04, 2008 6:41 am UTC

### Re: 1204: "Detail"

Kit. wrote:Then you should probably tell all the imaging sensors manufacturers around the world that they are doing it wrong.

As is pointed out in the memo, imaging sensor manufacturers are doing it very much right. Real sensors sample points (sometimes, in colour or other multispectral sensors, there are multiple distinct but close points), after the physics of the sensor and optical system have convolved the signal with a sampling kernel first.

It's difficult to see how you could construct an imaging sensor which integrates with uniform weight over a square (or rectangular) support. It's even more difficult to see anyone would bother to construct such a sensor. Real optical systems tend to be isotropic (which shouldn't be surprising), which squares and rectangles are not. Moreover, they are often well-approximated by a Gaussian for the same reason why the central limit theorem works: a bunch of uncorrelated imperfect optical stages put on top of each other tends to be Gaussian in the limit.

Actaeus
Posts: 606
Joined: Thu Jan 10, 2008 9:21 pm UTC
Location: ZZ9 Plural Z Alpha

### Re: 1204: "Detail"

da Doctah wrote:
Davidy wrote:Someone should contact Stephen Wright. He has a head start with his map of the United States with a 1:1 scale.

Which he stole from Lewis Carroll.

…from Sylvie and Bruno Concluded, by Lewis Carroll, 1893…

‘That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

“About six inches to the mile.”

“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”

“Have you used it much?” I enquired.

“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

I was going to accuse Carroll of ripping off Borges (On Exactitude in Science), but that was written in 1946:
Jorge Luis Borges wrote:
. . . In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

Suarez Miranda,Viajes de varones prudentes, Libro IV,Cap. XLV, Lerida, 1658

endolith
Posts: 229
Joined: Tue Jan 01, 2008 2:14 am UTC
Location: New York, NY
Contact:

### Re: 1204: "Detail"

Afrael wrote:Pardon my question.

Does the fact that Randall is using a log scale mean he is projecting an exponential growth of precision? Is that anywhere close to realistic?

PROTIP: Usually, exponential growth is just the first stage of logistic growth, which does not increase without bound or result in "singularities".

endolith
Posts: 229
Joined: Tue Jan 01, 2008 2:14 am UTC
Location: New York, NY
Contact:

### Re: 1204: "Detail"

Wooloomooloo wrote:That paper is right that you need to think of pixels as point samples rather than small rectangles if you do image processing (including various rescaling etc.); which is nitpicking inasmuch that more mundane tasks involving images - like displaying them in a piece of software (copying / laying out the data in a grid) or editing them as super-high-zoom art ("pixel art") - can and does use the rectangle concept quite successfully.

The "rectangle concept" is just nearest-neighbor interpolation of the point sample pixels. Other interpolations are also valid, such as bicubic interpolation. The pixels are still points either way.

The dots are the pixels, the colored parts are the interpolation. Images are not usually anti-aliased before sampling, so the sampling theorem is not totally valid for images, and you can get Moiré effects when the subject detail is finer than the resolution of the image.

On the other hand, the imaging sensor in a camera really does use tiny little rectangles, and those are called pixels. But there's no reason why they couldn't be arranged in triangles or as hexagons, and they would still be called pixels.

EpicanicusStrikes
Random Boners = True Attraction
Posts: 130
Joined: Wed Nov 16, 2011 11:36 am UTC

### Re: 1204: "Detail"

Fire Brns wrote:the "plank" part was still the focus of it. It was wrong regardless.

Planck lengths are more than just arbitrary units intended to provide a standard frame of reference. They are a function of the relationship between the frequency and wavelength of light. Nearly every intelligible quantum theory recognizes them as the smallest possible unit of measurement (or at least the smallest unit at which any reaction of consequence can occur).

If not for them, we would not have this ordered universe to play with.

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

### Re: 1204: "Detail"

DeGuerre wrote:
Kit. wrote:Microsoft at its... well, not exactly worst, but you got the idea.

Actually, Alvy Ray Smith wrote the first version of that memo when he was working at Pixar. You might want to rethink your company prejudice.

I don't see how it would help your case, as I also have a prejudice against Pixar

But anyway, for Pixar, which at the moment had no relation to image acquisition business (as far as I know), his memo might have a point (but he still shouldn't have called those his entities "pixels"). For Microsoft, it wouldn't.

DeGuerre wrote:
Kit. wrote:
lgw wrote:The worst way to sample is to divide the image into cells and then represent each cell as a number - that forces aliasing into the stored image.
Then you should probably tell all the imaging sensors manufacturers around the world that they are doing it wrong.

As is pointed out in the memo, imaging sensor manufacturers are doing it very much right.

I have restored the quote I was answering to.

There were technologies that weren't "to divide the image into cells and then represent each cell as a number" (silver halide film has already been mentioned) - but, unfortunately, they have proved to be worse.

DeGuerre wrote:Real sensors sample points (sometimes, in colour or other multispectral sensors, there are multiple distinct but close points), after the physics of the sensor and optical system have convolved the signal with a sampling kernel first.

No, real sensors don't sample points. Saying that "sensor readings can theoretically be mapped into sample points of some imaginary subjects", while being technically correct by itself, doesn't help either, because it's exactly how aliasing is introduced in the first place.

DeGuerre wrote:It's difficult to see how you could construct an imaging sensor which integrates with uniform weight over a square (or rectangular) support. It's even more difficult to see anyone would bother to construct such a sensor.

So, is it difficult for you to understand why photo sensor manufacturers employ microlenses over square pixels on their sensors?

DeGuerre wrote:Real optical systems tend to be isotropic (which shouldn't be surprising), which squares and rectangles are not. Moreover, they are often well-approximated by a Gaussian for the same reason why the central limit theorem works: a bunch of uncorrelated imperfect optical stages put on top of each other tends to be Gaussian in the limit.

Please don't tell me that you have never observed the real effects of the optical aberrations.

endolith wrote:On the other hand, the imaging sensor in a camera really does use tiny little rectangles, and those are called pixels. But there's no reason why they couldn't be arranged in triangles or as hexagons, and they would still be called pixels.

That's the traditional ("normal" for me) meaning of the term. Fujifilm used to make sensors with octagonal pixels, but wasn't particularly successful. There are also some patents for sensors with hexagonal pixels, but I'm not aware of such sensors in production.

lgw
Posts: 437
Joined: Mon Apr 12, 2010 10:52 pm UTC

### Re: 1204: "Detail"

Kit. wrote:
lgw wrote:When that was written, a pixel was three lights, each a different color, somewhat near one another.

A pixel has never been "three lights".

When that was written, I was working with pixels that were unweighted grayscale averages over cells in a rectangular grid. They had been basically this way since the word "pixel" was introduced.

A "pixel" can refer to the input (camera/sensor) format, the abstract image representation, or the display format. On the display they are usually three separate lights! That's why sub-pixel rendering is cool. (EDIT: unless you're talking about greyscale monochrome monitors? Were those ever common, besides the original Mac? I remember a mix of greenscreen and TV monitors early on.)

Kit. wrote:
lgw wrote:But regardless, "a little square" is a terrible way to think of a pixel in a stored image format. A pixel is a sample of the image centered at a point.

Nope, a pixel in an digitized image is not a point sample. It's an average over area, and the area may not even have a single point represented by the resulting value (usual for images innately monochrome on micro-level, like images acquired from silver photo film or fingerprint images or re-scanned images of dithered single-ink prints).

It's an average over an area, an area with a center, a center that is a point. Thus it's a sample of the image, centered at a point. Often the points-that-are-the-centers-of-the-samples-of-the-image are arranged in a rectangular grid. In a cool image format, the area of each sample is much larger than the space between those centers (the samples overlap), so if the display has a different rectangular grid than the image format (or the input format) you have less trouble with artifacts.

Kit. wrote:
lgw wrote:The worst way to sample is to divide the image into cells and then represent each cell as a number - that forces aliasing into the stored image.

Then you should probably tell all the imaging sensors manufacturers around the world that they are doing it wrong.

And when you want to represent the raw data from that sensor in some image format of reasonable size? A good digital image format makes the translation from the input format to the output format as lossless and artifact-free as possible, while being of reasonable size. Dividing the input up into little rectangles and representing each as a number is a bad way of doing that, was the authors point.
"In no set of physics laws do you get two cats." - doogly

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

### Re: 1204: "Detail"

lgw wrote:
Kit. wrote:
lgw wrote:When that was written, a pixel was three lights, each a different color, somewhat near one another.

A pixel has never been "three lights".

When that was written, I was working with pixels that were unweighted grayscale averages over cells in a rectangular grid. They had been basically this way since the word "pixel" was introduced.

A "pixel" can refer to the input (camera/sensor) format, the abstract image representation, or the display format. On the display they are usually three separate lights! That's why sub-pixel rendering is cool.

Not at that time. There are 6(!) different ways to combine the nearest color dot triangles on shadow masks monitors into rectangular grids. And not a single one of them is more "native" than another.

Besides, I don't like your classification, it's missing one very important point. See below.

lgw wrote:
Kit. wrote:
lgw wrote:But regardless, "a little square" is a terrible way to think of a pixel in a stored image format. A pixel is a sample of the image centered at a point.

Nope, a pixel in an digitized image is not a point sample. It's an average over area, and the area may not even have a single point represented by the resulting value (usual for images innately monochrome on micro-level, like images acquired from silver photo film or fingerprint images or re-scanned images of dithered single-ink prints).

It's an average over an area, an area with a center, a center that is a point. Thus it's a sample of the image, centered at a point. Often the points-that-are-the-centers-of-the-samples-of-the-image are arranged in a rectangular grid. In a cool image format, the area of each sample is much larger than the space between those centers (the samples overlap), so if the display has a different rectangular grid than the image format (or the input format) you have less trouble with artifacts.

If we are speaking about an uniform averaging, the "centered at a point" part is useless, it bears exactly 0 bits of information. But "out-of-band" (so to speak) it communicates that someone is very likely to confuse imprecise real-world images and underspecified computer art.

That's the difference between two types of "image representation" you forgot to separate in your classification. There are area-averaged images (with not always known ways of averaging), and there are computer art point samples (usually without a specified interpolation function). They are clearly distinct, and it can be easily demonstrated by their "natural" ways of downsampling: you average the cell values in area-averaged images, and you throw away the unneeded point values in point sample images.

Now, about your "cool image format": you can convert an area grid into it at any moment. The problem is: once you need the resolution (see what the comic page is about), you will need to convert your format back into the area grid, and this conversion pair is lossy.

lgw wrote:
Kit. wrote:
lgw wrote:The worst way to sample is to divide the image into cells and then represent each cell as a number - that forces aliasing into the stored image.

Then you should probably tell all the imaging sensors manufacturers around the world that they are doing it wrong.

And when you want to represent the raw data from that sensor in some image format of reasonable size?

First, you need to acquire it.

While capturing a single photon into different cells of different sizes and/or placements (multielectron absorption) is theoretically possible, it's well beyond any foreseeable imaging technology. And the attempts to fine-tune the coordinates of single photons hitting the sensor would just lead to the same rectangular grids, just finer-spaced.

As for the computer art, it just needs to be kept in the format it was rendered from.

Angelastic
Posts: 700
Joined: Thu Nov 03, 2011 8:36 am UTC
Location: .at (let's see what's through here!)
Contact:

### Re: 1204: "Detail"

lgw wrote:greyscale monochrome monitors? Were those ever common, besides the original Mac?
Several early PowerBooks (from the 150 onwards, up to the low-end 5300 in 1995, as far as I can tell) had greyscale monitors. The original Mac was black & white, as was my PowerBook 145B (missed out on two-bit grayscale by that much.)
Knight Temporal, and Archdeacon of buttermongery and ham and cheese sandwiches. Nobody sells butter except through me.
Smiley by yappobiscuits. Avatar by GLR, buffygirl, BlitzGirl & mscha, with cari.j.elliot's idea.
Haiku Detector
starts a trend to make way for
my robot army.

Fire Brns
Posts: 1114
Joined: Thu Oct 20, 2011 2:25 pm UTC

### Re: 1204: "Detail"

EpicanicusStrikes wrote:
Fire Brns wrote:the "plank" part was still the focus of it. It was wrong regardless.

Planck lengths are more than just arbitrary units intended to provide a standard frame of reference.
I'm not saying that!!! What I was saying was that planck is spelled p-l-a-n-C-k NOT p-l-a-n-k.

...
Pfhorrest wrote:As someone who is not easily offended, I don't really mind anything in this conversation.
Mighty Jalapeno wrote:It was the Renaissance. Everyone was Italian.

DeGuerre
Posts: 51
Joined: Mon Feb 04, 2008 6:41 am UTC

### Re: 1204: "Detail"

Kit. wrote:I don't see how it would help your case, as I also have a prejudice against Pixar

Fair enough. So do I, as it happe.s

Kit. wrote:But anyway, for Pixar, which at the moment had no relation to image acquisition business (as far as I know),

They were upstream consumers. This was the days of CAPS, which relied on the best scanners that Disney could buy.

Kit. wrote:There were technologies that weren't "to divide the image into cells and then represent each cell as a number" (silver halide film has already been mentioned) - but, unfortunately, they have proved to be worse.

As noted, the problem with the claim is "divide the image into cells". Almost all image acquisition technologies return a weighted average over an area that overlaps with adjacent areas.

Kit. wrote:So, is it difficult for you to understand why photo sensor manufacturers employ microlenses over square pixels on their sensors?

Not at all. There are good reasons to do that. In almost all cases, those sensors are behind other optical elements which increase the effective support of the sample.

There are a few exceptions, like some non-laser, non-CCD film scanners. Even then, the good ones oversample and digitally filter the result.

lgw
Posts: 437
Joined: Mon Apr 12, 2010 10:52 pm UTC

### Re: 1204: "Detail"

Kit. wrote:
lgw wrote:It's an average over an area, an area with a center, a center that is a point. Thus it's a sample of the image, centered at a point. Often the points-that-are-the-centers-of-the-samples-of-the-image are arranged in a rectangular grid. In a cool image format, the area of each sample is much larger than the space between those centers (the samples overlap), so if the display has a different rectangular grid than the image format (or the input format) you have less trouble with artifacts.

If we are speaking about an uniform averaging, the "centered at a point" part is useless, it bears exactly 0 bits of information. But "out-of-band" (so to speak) it communicates that someone is very likely to confuse imprecise real-world images and underspecified computer art.

That's the difference between two types of "image representation" you forgot to separate in your classification. There are area-averaged images (with not always known ways of averaging), and there are computer art point samples (usually without a specified interpolation function). They are clearly distinct, and it can be easily demonstrated by their "natural" ways of downsampling: you average the cell values in area-averaged images, and you throw away the unneeded point values in point sample images.

Now, about your "cool image format": you can convert an area grid into it at any moment. The problem is: once you need the resolution (see what the comic page is about), you will need to convert your format back into the area grid, and this conversion pair is lossy.

OK, I get the distinction you're making, but it's different from the distinction I was making - let's ignore the "computer art" silly method. Let's say we have a very high resolution monochrome original that we're trying to downsample into a low resolution - but grayscale - stored image. Whatever we do will be lossy.
• One approach is to divide the original into square cells, and record the grayness of each cell (perhaps one cell is 40x40 in the monochrome original, so we map the value from 0 to 1600 into a byte) - we think of a pixel as a little square.
• Another approach is to choose a grid of evenly spaced points (perhaps every 40 original-resolution-dots apart), then take a weighted average of the grayness of the whole image as centered on that point (perhaps 1/r2) - quite computationally intensive - or just a weighted average "near" each point, less computationally intensive. Our pixels overlap.
• Another approach is to create a holograph of the original and digitize that, or otherwise digitize an unfocused image, and figure out the focus later. Our pixels may each describe the whole image in some way. The software around "focus after the fact" has recently gotten a lot of attention (though I suspect it's old hat for spy satellites).

If we have the same resolution and grayscale depth on each format, we should be able to reconstruct an image for display with the similar lossiness, but each will be lossy in different ways. If we have a color image, represented as a set of color planes, and our display has an offset for different colors (red subpixels to the left of blue, or whatever), then the second can do better. Each approach has some strengths and weaknesses.
"In no set of physics laws do you get two cats." - doogly