12 ms·

Pixel is a unit of length and area

145 points by anitil 1y ago

deleted 1y ago
[deleted]
anitil 1y ago
This is a fun post by Nayuki - I'd never given this much thought, but this takes the premise and runs with it
knallfrosch 1y ago
Happens to all square shapes. A chessboard is 8 tiles wide and 8 tiles long, so it consists of 64 tiles covering an area of, well, 64 tiles.
- pvdebbe 1y ago
  City blocks, too.
  - Aldipower 1y ago
    In the US...
    - jeltz 1y ago
      While it is certainly more common in the US we occasionally use blocks as a measurement here in Sweden too. Blocks are just smaller and less regular here.
    - matthewowen 1y ago
      Do people in Spanish cities with strong grids (eg Barcelona) not also use the local language equivalent of "blocks" as a term? I would be surprised if not. It's a fundamentally convenient term in any area that has a repeated grid. The fact that some cities don't have repeated grids and hence don't use the term is not really a valuable corrective to the post you are replying to.
      - mzs 1y ago
        In Slavic languages we think in terms of intersections for distance, maybe the same for Spanish? Area is thought of either as inside district (say city enter) or in meters squared.
        SAI_Peregrinus 1y ago
        A block is just the distance from one intersection to the next. Even if those distances vary or are non-square. E.g. Manhattan has mostly rectangular blocks, if you go from 8th Avenue to Madison Avenue along 39th St you traveled 4 blocks (the last of which is shorter than the first 3), if you go from 36th St to 40th St along 8th Avenue you traveled 4 blocks (all of which are shorter than the blocks between the avenues).
- HPsquared 1y ago
  Not all pixels are square, though! Does anyone remember anamorphic DVDs? https://en.wikipedia.org/wiki/Anamorphic_widescreen https://en.wikipedia.org/wiki/Anamorphic_widescreen
  - nayuki 1y ago
    Never mind anamorphic DVDs, all of them use non-square pixels. The resolution of DVD is 720×480 pixels (or squared pixels, referring back to the article); this is a 3:2 ratio of pixel quantities on the horizontal vs. vertical axes. But the overall aspect ratio of the image is displayed as either 4:3 (SDTV) or 16:9 (HDTV), neither of which matches 3:2. Hence the pixel aspect ratio is definitely not 1:1.
thehours 1y ago
Reminds me of this Numberphile w/ Cliff Stoll [1]: The Nescafé Equation (43 coffee beans) [1] https://youtu.be/3V84Bi-mzQM https://youtu.be/3V84Bi-mzQM
surfingdino 1y ago
A pixel is a sample or a collection of values of the Red, Green, and Blue components of light captured at a particular location in a typically rectangular area. Pixels have no physical dimensions. A camera sensor has no pixels, it has photosites (four colour sensitive elements per one rectangular area).
- danwills 1y ago
  Is a pixel not a pixel when it's in a different color space? (HSV, XYZ etc?)
  - surfingdino 1y ago
    RGB is the most common colour space, but yes, other colour spaces are available.
- echoangle 1y ago
  And what’s the difference between a photosite and a pixel? Sounds like a difference made up to correct other people.
  - surfingdino 1y ago
    A photosite is a set of four photosensitive electronic sensors that register levels of RGB components of light https://www.cambridgeincolour.com/tutorials/camera-sensors.htm https://www.cambridgeincolour.com/tutorials/camera-sensors.h... The camera sensor turns data captured by a a single photosite into a single data structure (a pixel), a tuple of as many discreet values as there are components in a given colour space (three for RGB).
    - echoangle 1y ago
      If you want to be pedantic, you shouldn’t say that the photosite has 4 sensors, depending on the color filter array you can have other numbers like 9 or 36, too. And the difference is pure pedantry, because each photosite corresponds to a pixel in the image (unless we’re talking about lens correction?). It’s like making up a new word for monitor pixels because those are little lights (for OLED) while the pixel is just a tuple of numbers. I don’t see why calling the sensor grid items „pixels“ is misunderstandable in any way.
Sharlin 1y ago
Pixel, used as a unit of horizontal or vertical resolution, typically implies the resolution of the other axis as well, at least up to common aspect ratios. We used to say 640x480 or 1280x1024 – now we might say 1080p or 2.5K but what we mean is 1920x1080 and 2560x1440, so "pixel" does appear to be a measure of area. Except of course it's not – it's a unit of a dimensionless quantity that measures the amount of something, like the mole. Still, a "quadratic count" is in some sense a quantity distinct from "linear count", just like angles and solid angles are distinct even though both are dimensionless quantities. The issue is muddied by the fact that what people mostly care about is either the linear pixel count or pixel pitch, the distance between two neighboring pixels (or perhaps rather its reciprocal, pixels per unit length). Further confounding is that technically, resolution is a measure of angular separation, and to convert pixel pitch to resolution you need to know the viewing distance. Digital camera manufacturers at some point started using megapixels (around the point that sensor resolutions rose above 1 MP), presumably because big numbers are better marketing. Then there's the fact that camera screen and electronic viewfinder resolutions are given in subpixels, presumably again for marketing reasons.
- HPsquared 1y ago
  Digital photography then takes us on to subpixels, Bayer filters (https://en.wikipedia.org/wiki/Color_filter_array https://en.wikipedia.org/wiki/Color_filter_array) and so on. You can also divide the luminance colour parts out. Most image and video compression puts more emphasis on the luminance profile, getting the colour more approximate. The subpixels on a digital camera (or a display for that matter) take advantage of this quirk of human vision.
forrestthewoods 1y ago
I’m surprised the author didn’t dig into the fact that not all pixels are square. Or that pixels are made of underlying RGB light emitters. And that those RGB emitters are often very non-square. And often not 1:1 RGBEmitter-to-Pixel (stupid pentile).
- petesergeant 1y ago
  > "Je n’ai fait celle-ci plus longue que parce que je n’ai pas eu le loisir de la faire plus courte." or > "I have made this longer than usual because I have not had time to make it shorter."
  - forrestthewoods 1y ago
    I love that quote. But that’s the opposite.
- nayuki 1y ago
  Or the fact that a 1 megapixel camera (counting each color-filtered sensing element as a pixel) generates less information than a 1 megapixel monitor (counting each RGB triad as a pixel) can display.
Laremere 1y ago
I'd say it's better to call it a unit of counting. If I have a bin of apples, and I say it's 5 apples wide, and 4 apples tall, then you'd say I have 20 apples, not 20 apples squared. It's common to specify a length by a count of items passed along that length. Eg, a city block is a ~square on the ground bounded by roads. Yet if you're traveling in a city, you might say "I walked 5 blocks." This is a linguistic shortcut, skipping implied information. If you're trying to talk about both in a unclear context, additional words to clarify are required to sufficiently convey the information, that's just how language words.
- petesergeant 1y ago
  Is it that, or is it a compound unit that has a defined width and height already? Something can be five football fields long by two football fields wide, for an area of ten football fields.
  - jeltz 1y ago
    No, it is a count. Pixels can have different sizes and shapes, just like apples. Technically football fields vary slightly too but not close to as much as apples or pixels.
    - petesergeant 1y ago
      What's the standard size of a city block, the other countable example given by the original author?
      - jeltz 1y ago
        Yes, city blocks are like pixels or apples. They do not have a standard size or shape. Edit: To clarify, if someone says 3 blocks that could vary by like a factor of like 3 or in extreme caesx more so when used as a unit of length it is a very rough estimate. It is usually used in my country as a way to know when you have reached your destination.
    - HelloNurse 1y ago
ttoinou 1y ago
But it does highlight that the common terminology is imperfect and breaks the regularity that scientists come to expect when working with physical units in calculations Scientists and engineers dont actually expect much, they make a lot of mistakes, are not very rigorous, not demanding towards each others. It is common for Units to be wrong, context defined, socially dependent and even sometimes added together when the operator + hasn't been properly defined
GuB-42 1y ago
A pixel is neither a unit of length nor area, it is like a byte, a unit of information. Sometimes, it is used as a length or area, omitting a conversion constant, but we do it all the times, the article gives out the mass vs force as an example. Also worth mentioning that pixels are not always square. For example, the once popular 320x200 resolution have pixels taller than they are wide.
- nayuki 1y ago
  It's not a unit of information. How many bytes does a 320×240 image take? You don't know until you specify the pixel bit depth in bpp (bits per pixel).
justin_ 1y ago
> A Pixel Is Not A Little Square! > This is an issue that strikes right at the root of correct image (sprite) computing and the ability to correctly integrate (converge) the discrete and the continuous. The little square model is simply incorrect. It harms. It gets in the way. If you find yourself thinking that a pixel is a little square, please read this paper. > A pixel is a point sample. It exists only at a point. For a color picture, a pixel might actually contain three samples, one for each primary color contributing to the picture at the sampling point. We can still think of this as a point sample of a color. But we cannot think of a pixel as a square—or anything other than a point. Alvy Ray Smith, 1995 http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
- toxik 1y ago
  This is one of my favorite articles. Although I think you can define for yourself what your pixels are, for most it is a point sample.
- Veedrac 1y ago
  A pixel is simply not a point sample. A camera does not take point sample snapshots, it integrates lightfall over little rectangular areas. A modern display does not reconstruct an image the way a DAC reconstructs sounds, they render little rectangles of light, generally with visible XY edges. The paper's claim applies at least somewhat sensibly to CRTs, but one mustn't imagine the voltage interpolation and shadow masking a CRT does corresponds meaningfully to how modern displays work... and even for CRTs it was never actually correct to claim that pixels were point samples. It is pretty reasonable in the modern day to say that an idealized pixel is a little square. A lot of graphics operates under this simplifying assumption, and it works better than most things in practice.
  - gugagore 1y ago
    DACs do a zero-order hold, which is equivalent to a pixel as a square.
    - 1y ago
Aldipower 1y ago
A Pixel is a telephone.
JimDabell 1y ago
This depends upon who you ask. CSS defines a pixel as an angle: https://www.w3.org/TR/css-values-3/#reference-pixel https://www.w3.org/TR/css-values-3/#reference-pixel
- didroe 1y ago
  That's the definition of a "reference pixel", not a pixel. They actually refer to a pixel (and the angle) in the definition.
ChrisMarshallNY 1y ago
A pixel is a dot. The size and shape of the dot is implementation-dependent. The dot may be physically small, or physically large, and it may even be non-square (I used to work for a camera company that had non-square pixels in one of its earlier DSLRs, and Bayer-format sensors can be thought of as “non-square”), so saying a pixel is a certain size, as a general measure across implementations, doesn’t really make sense. In iOS and MacOS, we use “display units,” which can be pixels, or groups of pixels. The ratio usually changes, from device to device.
- Y-bar 1y ago
  This is my favourite single-pixel interface: https://en.wikipedia.org/wiki/Trafficators https://en.wikipedia.org/wiki/Trafficators
  - ChrisMarshallNY 1y ago
    They are sort of coming back, as side-mirror indicators.
ivan_gammel 1y ago
So, the author answers the question: > That means the pixel is a dimensionless unit that is just another name for 1, kind of like how the radian is length divided by length so it also equals one, and the steradian is area divided by area which also equals one. But then for some reason decides to ignore it. I don’t understand this article. Yes, pixels are dimensionless units used for counting, not measuring. Their shape and internal structure is irrelevant (even subpixel rendering doesn’t actually deal with fractions - it alters neighbors to produce the effect).
blenderob 1y ago
The article starts out with an assertion right in the title and does not do enough to justify it. The title is just wrong. Saying pixels are like metres is like saying metres are like apples. When you multiply 3 meter by 4 meter, you do not get 12 meters. You get 12 meter squared. Because "meter" is not a discrete object. It's a measurement. When you have points A, B, C. And you create 3 new "copies" of those points (by geometric manipulation like translating or rotating vectors to those points), you now have 12 points: A, B, C, A1, B1, C1, A2, B2, C2, A3, B3, C3. You don't get "12 points squared". (What would that even mean?) Because points are discrete objects. When you have 3 apples in a row and you add 3 more such rows, you get 4 rows of 3 apples each. You now have 12 apples. You don't have "12 apples squared". Because apples are discrete objects. When you have 3 pixels in a row and you add 3 more such rows of pixels, you get 4 rows of 3 pixels each. You now have 12 pixels. You don't get "12 pixels squared". Because pixels are discrete objects. Pixels are like points and apples. Pixels are not like metres.
- Izkata 1y ago
  > When you multiply 3 meter by 4 meter, you do not get 12 meters. You get 12 meter squared. "12 meter(s) squared" sounds like a square that is 12 meters on each side. On the other hand, "12 square meters" avoids this weirdness by sounding like 12 squares that are one meter on each side, which the area you're actually describing.
  - chii 1y ago
    that's just a quirk of the language. If you use formal notation, 12 m^2 is very clear. But i have yet to see anyone write 12px^2
    - Izkata 1y ago
      It's one that really bothers me because of the unnecessary confusion it adds. As for the rest, see GGP's argument. px^2 doesn't make logical sense. When people are use pixels as length, it's in the same way as "I live 2 houses over" - taking a 2D or 3D object and using one of its dimensions as length/distance.
tomhow 1y ago
See also: A Pixel Is Not a Little Square (1995) [pdf] – http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
- glitchc 1y ago
  This is written from a rather narrow perspective (of signal processing) and is clearly wrong in other contexts. For an image sensor designer, gate length, photosensitive area and pixel pitch are all real-valued measurements. That pixels are laid out on a grid simply reflects the ease of constructing electronic circuits this way. Alternative arrangements are possible, Sigma's depth pixels being one commercial example.
  - grandempire 1y ago
    Ok, but that’s not what an digital image is. Images are designed to be invariant across camera capture and display hardware. The panel driver should interpret the dsp representation into an appropriate electronic pixel output.
    - fluoridation 1y ago
      Well, "what a digital image is" is a sequence of numbers. There's no single correct way to interpret the numbers, it depends on what you want to accomplish. If your digital image is a representation of, say, the dead components in an array of sensors, the signal processing theoretic interpretation of samples may not be useful as far as figuring out which sensors you should replace.
      - grandempire 1y ago
        > There's no single correct way to interpret the numbers They are just bits in a computer. But there is a correct way of to interpret them in a particular context. For example 32 bits can be meaningless - or it can have an interpretation as a twos complement integer which is well defined. If you are looking to understand how an operating system will display images, or how graphics drivers work, or how photoshop will edit them, or what digital cameras produce, then it’s the point sample definition.
dullcrisp 1y ago
Wait till they hear about fluid ounces.
jrvieira 1y ago
The author is very confused.
gilgoomesh 1y ago
A pixel is two dimensional, by definition. It is a unit of area. Even in the signal processing "sampling" definition of a pixel, it still has an areal density an is therefore still two-dimensional. The problem in this article is it incorrectly assumes a pixel to be a length and then makes nonsensical statements. The correct way to interpret "1920 pixels wide" is "the same width as 1920 pixels arranged in a 1920 by 1 row". In the same way that "square feet" means "feet^2" as "square" acts as a square operator on "feet", in "pixels wide" the word "wide" acts as a square root operator on the area and means "pixels^(-2)" (which doesn't otherwise have a name).
- danbruc 1y ago
  It is neither a unit of length nor area, it is just a count, a pixel - ignoring the CSS pixel - has no inherent length or area. To get from the number of pixels to a length or area, you need the pixel density. 1920 pixel divided by 300 pixel per inch gives you the length of 6.4 inch and it all is dimensionally consistent. The same for 18 mega pixel, with a density of 300 times 300 pixel per square inch you get an image area of 200 square inch. Here pixel per inch times pixel per inch becomes pixel per square inch, not square pixel per square inch.
  - deleted 1y ago
    [deleted]
- jillesvangurp 1y ago
  CSS got it right by making pixels a relative unit. Meters are absolute. You cannot express pixels in meters. Because they are relative units. If you have a high resolution screen the a CSS pixel is typically be 4 actual display pixels (2x2) instead of just 1. And if you change the zoom level, the amount of display pixels might actually change in fractional ways. The unit only makes sense in relation to what's around it. If you render vector graphics or fonts, pixels are used as relative units. On a high resolution screen it will actually use those extra display pixels. If you want to show something that's exactly 5cm on a laptop or phone screen, you need to know the dimensions of the screen and figure out how many pixels you need per cm to scale things correctly. Css has some absolute units but they only work as expected for print media typically.
bitwize 1y ago
Pixels are not measurement units. They're samples of an image taken a certain distance apart. It's like eggs in a carton: it's perfectly legitimate to say that a carton is 6 eggs long and 3 eggs wide, and holds a total of 18 eggs, because eggs are counted, they're not a length measure except in the crudest sense.
otikik 1y ago
Well the way I see them I don't think they are a unit at all. And the end pixels are "physical things". Like ceramic tiles on a bathroom wall. Your wall might be however many meters in length and you might need however squared meters of tile in order to cover it. But still, if you need 10 tiles high and 20 tiles width, you need 200 tiles to cover it. No tension there. Now you might argue that pixels in a scaled game don't correspond with physical objects in the screen any more. That's ok. A picture of the bathroom wall will look smaller than the wall itself. Or bigger, if you hold it next to your face. It's still 10x20=200 tiles.
fennecbutt 1y ago
Or perhaps it's multivariate and there's no point in trying to squish all the nuance into a single solid definition.
RedNifre 1y ago
What a perplexing article. Isn't a pixel clearly specified as a picture element? Isn't the usage as a length unit just as colloquial as "It's five cars long", which is just a simplified way of saying "It is as long as the length of a car times five", where "car" and "length of car" are very clearly completely separate things? > The other awkward approach is to insist that the pixel is a unit of length Please don't. If you want a unit of length that works well with pixels, you can use Android's "dp" concept instead, which are "density independent pixels" (kinda a bad name if you think about it) and are indeed a unit of length, namely 1dp = 158.75 micro meter, so that you have 160 dp to the inch. Then you can say "It's 10dp by 5dp, so 50 square dp in area.".
- tshaddox 1y ago
  Yeah, this isn't really that complicated. It's just colloquial usage, not rigorous dimensional analysis. Roughly no one is actually confused by either usage ("1920 by 1080" or "12 megapixels"). It's nearly identical to North American usage of "block" (as in "city block"). Merriam Webster lists these two definitions (among many others): > 6 a (1): a usually rectangular space (as in a city) enclosed by streets and occupied by or intended for buildings > 6 a (2): the distance along one of the sides of such a block
- munk-a 1y ago
  Another colloquial saying to back this up is that "Oh, that house is five acres down the road" or, for a non-standard unit, "The store is three blocks away". We often use area measurements for length if it's convenient. The pixel is a unit of area - we just occasionally use units of area to measure length.
  - JadeNB 1y ago
    > Another colloquial saying to back this up is that "Oh, that house is five acres down the road" or, for a non-standard unit, "The store is three blocks away". We often use area measurements for length if it's convenient. I have never heard someone use the first instance, and I wouldn't understand what it meant. I mean, I could buy that it meant that there is a five-acre plot between that house and where we are now, but it wouldn't give me any useful idea of how far the house is other than "not too close." Perhaps you have in mind that, since the "width" of an acre is a furlong, a house 5 acres away is 5 furlongs away?
rbanffy 1y ago
For those who programmed 8-bit computers or worked with analog video, a pixel is also a unit of time. An image is a long line with some interruptions.
deleted 1y ago
[deleted]
jmull 1y ago
Hopefully most people get that the exact meaning of "pixel" depends on context? It certainly doesn't make sense to mix different meanings in a mathematical sense. E.g., when referring to a width in pixels, the unit is pixel widths. We shorten it and just say pixels because it's awkward and redundant to say something like "the screen has a width of 1280 pixel widths", and the meaning is clear to the great majority of readers.
_wire_ 1y ago
This article wastes readers' time by pretending to command of a subject in a manner that is authoritative only in its uncertainty. Pixel is an abbreviation for 'picture element' which describes a unit of electronic image representation. To understand it, consider picture elements in the following context... (Insert X different ways of thinking about pictures and their elements.) If there is a need for a jargon of mathematical "dimensionality" for any of these ways of thinking, please discuss it in such context. Next up: <i>A musical note is a unit of...</i>
scotty79 1y ago
Pixel is just contextual. When you are talking about one dimensional things it's a unit of length. In all mother cases it's a unit of area.
teknopaul 1y ago
The pixel ain't no problem. A "megapixel" is simply defined as 1024 pixels squared ish. There is no kilopixel. Or exapixel. No-one doesn't understand this?
webstrand 1y ago
This kind of thing is common in english, though. "an aircraft carrier is 3.5 football fields long" The critical distinction is the inclusion of a length dimension in the measurement: "1920 pixels wide", "3 mount everests tall", "3.5 football fields long", etc.
jefftk 1y ago
This isn't just pixels, it's the normal way we use rectangular units in common speech: * A small city might be ten blocks by eight blocks, and we could also say the whole city is eighty blocks. * A room might by 13 tiles by 15 tiles, or 295 tiles total. * On graph paper you can draw a rectangle that's three squares by five squares, or 15 squares total.
tuzemec 1y ago
Also a measurement of life. Back in the 320x200 game days, when playing something with a health bar, we used to joke that someone had one pixel of life left when near death.
alzamixer 1y ago
Should be pixel as area and pixel-length as 1-dimensional unit. So an image could be 1 mega pixel, or 1000 times 1000 pixel-lengths.
nout 1y ago
Pixel is also a unit of a phone.
kazinator 1y ago
A bathroom tile is also a unit of length and area. A wall can be so many tiles high by so many wide, and its area the product, also measured in tiles. It is just word semantics revolving around a synecdoche. When we say that an image is 1920 pixels wide, the precise meaning is that it is 1920 times the width of a pixel. Similarly 1024 pixels high means 1024 times the height of a pixel. The pixel is not a unit of length; its height or width are (and they are different when the aspect ratio is not 1:1!) A syntax-abbreviating semantic device in human language where part of something refers to the whole or vice versa is called a synecdoche. Under synecdoche, "pixel" (the whole) can refer to "pixel width" (part or property of the whole). Just like the synecdoche "New York beats Chicago 4:2" refer to basketball teams in its proper context, not literally the cities.
dusted 1y ago
I think the author forgets that pixels inherently have both width and height, a single pixel, is inherently a 2 dimensional entity, whereas the meter is a purely one dimensional concept. You don't usually talk about whether your meters are the same height as they are tall, or whether they're taller than they're wide.. because they don't have those two dimensions.. You don't talk about how your centimeters are arranged within your meter either.. (you can talk about how your subpixels are, and even if there are 3 or 4 of them). So, I don't think it's entirely valid to talk about pixels as if they are pure, one dimensional units.. They're _things_ and you can talk about how many things wide or tall something is, and you can talk about how many things something has. Very much the same way you can with bricks (which are mostly never square) (though tiles are, you never talk about how many kilotiles is in your bathroom either, yet you can easily talk about how many tiles wide or tall a wall is). So, no, pixels is not a unit in the mathematical sense.. it's an item, in the physical sense. There are also things like scanners, that may have only one row of pixels on the scanner sensor, it does not have an area of zero, and you don't need to specify that there's one pixel on the other axis, because it's an inherent property of pixels that they have both width and height and thus area in and of themselves.

145 points by anitil 1y ago

deleted 1y ago

[deleted]

anitil 1y ago

This is a fun post by Nayuki - I'd never given this much thought, but this takes the premise and runs with it

knallfrosch 1y ago

Happens to all square shapes. A chessboard is 8 tiles wide and 8 tiles long, so it consists of 64 tiles covering an area of, well, 64 tiles.

pvdebbe 1y ago
City blocks, too.
- Aldipower 1y ago
  In the US...
  - jeltz 1y ago
    While it is certainly more common in the US we occasionally use blocks as a measurement here in Sweden too. Blocks are just smaller and less regular here.
  - matthewowen 1y ago
    Do people in Spanish cities with strong grids (eg Barcelona) not also use the local language equivalent of "blocks" as a term? I would be surprised if not. It's a fundamentally convenient term in any area that has a repeated grid. The fact that some cities don't have repeated grids and hence don't use the term is not really a valuable corrective to the post you are replying to.
    - mzs 1y ago
      In Slavic languages we think in terms of intersections for distance, maybe the same for Spanish? Area is thought of either as inside district (say city enter) or in meters squared.
      - SAI_Peregrinus 1y ago
        A block is just the distance from one intersection to the next. Even if those distances vary or are non-square. E.g. Manhattan has mostly rectangular blocks, if you go from 8th Avenue to Madison Avenue along 39th St you traveled 4 blocks (the last of which is shorter than the first 3), if you go from 36th St to 40th St along 8th Avenue you traveled 4 blocks (all of which are shorter than the blocks between the avenues).
HPsquared 1y ago
Not all pixels are square, though! Does anyone remember anamorphic DVDs? https://en.wikipedia.org/wiki/Anamorphic_widescreen https://en.wikipedia.org/wiki/Anamorphic_widescreen
- nayuki 1y ago
  Never mind anamorphic DVDs, all of them use non-square pixels. The resolution of DVD is 720×480 pixels (or squared pixels, referring back to the article); this is a 3:2 ratio of pixel quantities on the horizontal vs. vertical axes. But the overall aspect ratio of the image is displayed as either 4:3 (SDTV) or 16:9 (HDTV), neither of which matches 3:2. Hence the pixel aspect ratio is definitely not 1:1.

thehours 1y ago

Reminds me of this Numberphile w/ Cliff Stoll [1]: The Nescafé Equation (43 coffee beans) [1] https://youtu.be/3V84Bi-mzQM https://youtu.be/3V84Bi-mzQM

surfingdino 1y ago

A pixel is a sample or a collection of values of the Red, Green, and Blue components of light captured at a particular location in a typically rectangular area. Pixels have no physical dimensions. A camera sensor has no pixels, it has photosites (four colour sensitive elements per one rectangular area).

danwills 1y ago
Is a pixel not a pixel when it's in a different color space? (HSV, XYZ etc?)
- surfingdino 1y ago
  RGB is the most common colour space, but yes, other colour spaces are available.
echoangle 1y ago
And what’s the difference between a photosite and a pixel? Sounds like a difference made up to correct other people.
- surfingdino 1y ago
  A photosite is a set of four photosensitive electronic sensors that register levels of RGB components of light https://www.cambridgeincolour.com/tutorials/camera-sensors.htm https://www.cambridgeincolour.com/tutorials/camera-sensors.h... The camera sensor turns data captured by a a single photosite into a single data structure (a pixel), a tuple of as many discreet values as there are components in a given colour space (three for RGB).
  - echoangle 1y ago
    If you want to be pedantic, you shouldn’t say that the photosite has 4 sensors, depending on the color filter array you can have other numbers like 9 or 36, too. And the difference is pure pedantry, because each photosite corresponds to a pixel in the image (unless we’re talking about lens correction?). It’s like making up a new word for monitor pixels because those are little lights (for OLED) while the pixel is just a tuple of numbers. I don’t see why calling the sensor grid items „pixels“ is misunderstandable in any way.

Sharlin 1y ago

Pixel, used as a unit of horizontal or vertical resolution, typically implies the resolution of the other axis as well, at least up to common aspect ratios. We used to say 640x480 or 1280x1024 – now we might say 1080p or 2.5K but what we mean is 1920x1080 and 2560x1440, so "pixel" does appear to be a measure of area. Except of course it's not – it's a unit of a dimensionless quantity that measures the amount of something, like the mole. Still, a "quadratic count" is in some sense a quantity distinct from "linear count", just like angles and solid angles are distinct even though both are dimensionless quantities. The issue is muddied by the fact that what people mostly care about is either the linear pixel count or pixel pitch, the distance between two neighboring pixels (or perhaps rather its reciprocal, pixels per unit length). Further confounding is that technically, resolution is a measure of angular separation, and to convert pixel pitch to resolution you need to know the viewing distance. Digital camera manufacturers at some point started using megapixels (around the point that sensor resolutions rose above 1 MP), presumably because big numbers are better marketing. Then there's the fact that camera screen and electronic viewfinder resolutions are given in subpixels, presumably again for marketing reasons.

HPsquared 1y ago
Digital photography then takes us on to subpixels, Bayer filters (https://en.wikipedia.org/wiki/Color_filter_array https://en.wikipedia.org/wiki/Color_filter_array) and so on. You can also divide the luminance colour parts out. Most image and video compression puts more emphasis on the luminance profile, getting the colour more approximate. The subpixels on a digital camera (or a display for that matter) take advantage of this quirk of human vision.

forrestthewoods 1y ago

I’m surprised the author didn’t dig into the fact that not all pixels are square. Or that pixels are made of underlying RGB light emitters. And that those RGB emitters are often very non-square. And often not 1:1 RGBEmitter-to-Pixel (stupid pentile).

petesergeant 1y ago
> "Je n’ai fait celle-ci plus longue que parce que je n’ai pas eu le loisir de la faire plus courte." or > "I have made this longer than usual because I have not had time to make it shorter."
- forrestthewoods 1y ago
  I love that quote. But that’s the opposite.
nayuki 1y ago
Or the fact that a 1 megapixel camera (counting each color-filtered sensing element as a pixel) generates less information than a 1 megapixel monitor (counting each RGB triad as a pixel) can display.

Laremere 1y ago

I'd say it's better to call it a unit of counting. If I have a bin of apples, and I say it's 5 apples wide, and 4 apples tall, then you'd say I have 20 apples, not 20 apples squared. It's common to specify a length by a count of items passed along that length. Eg, a city block is a ~square on the ground bounded by roads. Yet if you're traveling in a city, you might say "I walked 5 blocks." This is a linguistic shortcut, skipping implied information. If you're trying to talk about both in a unclear context, additional words to clarify are required to sufficiently convey the information, that's just how language words.

petesergeant 1y ago
Is it that, or is it a compound unit that has a defined width and height already? Something can be five football fields long by two football fields wide, for an area of ten football fields.
- jeltz 1y ago
  No, it is a count. Pixels can have different sizes and shapes, just like apples. Technically football fields vary slightly too but not close to as much as apples or pixels.
  - petesergeant 1y ago
    What's the standard size of a city block, the other countable example given by the original author?
    - jeltz 1y ago
      Yes, city blocks are like pixels or apples. They do not have a standard size or shape. Edit: To clarify, if someone says 3 blocks that could vary by like a factor of like 3 or in extreme caesx more so when used as a unit of length it is a very rough estimate. It is usually used in my country as a way to know when you have reached your destination.
  - HelloNurse 1y ago

ttoinou 1y ago

But it does highlight that the common terminology is imperfect and breaks the regularity that scientists come to expect when working with physical units in calculations Scientists and engineers dont actually expect much, they make a lot of mistakes, are not very rigorous, not demanding towards each others. It is common for Units to be wrong, context defined, socially dependent and even sometimes added together when the operator + hasn't been properly defined

GuB-42 1y ago

A pixel is neither a unit of length nor area, it is like a byte, a unit of information. Sometimes, it is used as a length or area, omitting a conversion constant, but we do it all the times, the article gives out the mass vs force as an example. Also worth mentioning that pixels are not always square. For example, the once popular 320x200 resolution have pixels taller than they are wide.

nayuki 1y ago
It's not a unit of information. How many bytes does a 320×240 image take? You don't know until you specify the pixel bit depth in bpp (bits per pixel).

justin_ 1y ago

> A Pixel Is Not A Little Square! > This is an issue that strikes right at the root of correct image (sprite) computing and the ability to correctly integrate (converge) the discrete and the continuous. The little square model is simply incorrect. It harms. It gets in the way. If you find yourself thinking that a pixel is a little square, please read this paper. > A pixel is a point sample. It exists only at a point. For a color picture, a pixel might actually contain three samples, one for each primary color contributing to the picture at the sampling point. We can still think of this as a point sample of a color. But we cannot think of a pixel as a square—or anything other than a point. Alvy Ray Smith, 1995 http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf

toxik 1y ago
This is one of my favorite articles. Although I think you can define for yourself what your pixels are, for most it is a point sample.
Veedrac 1y ago
A pixel is simply not a point sample. A camera does not take point sample snapshots, it integrates lightfall over little rectangular areas. A modern display does not reconstruct an image the way a DAC reconstructs sounds, they render little rectangles of light, generally with visible XY edges. The paper's claim applies at least somewhat sensibly to CRTs, but one mustn't imagine the voltage interpolation and shadow masking a CRT does corresponds meaningfully to how modern displays work... and even for CRTs it was never actually correct to claim that pixels were point samples. It is pretty reasonable in the modern day to say that an idealized pixel is a little square. A lot of graphics operates under this simplifying assumption, and it works better than most things in practice.
- gugagore 1y ago
  DACs do a zero-order hold, which is equivalent to a pixel as a square.
  - 1y ago

Aldipower 1y ago

A Pixel is a telephone.

JimDabell 1y ago

This depends upon who you ask. CSS defines a pixel as an angle: https://www.w3.org/TR/css-values-3/#reference-pixel https://www.w3.org/TR/css-values-3/#reference-pixel

didroe 1y ago
That's the definition of a "reference pixel", not a pixel. They actually refer to a pixel (and the angle) in the definition.

ChrisMarshallNY 1y ago

A pixel is a dot. The size and shape of the dot is implementation-dependent. The dot may be physically small, or physically large, and it may even be non-square (I used to work for a camera company that had non-square pixels in one of its earlier DSLRs, and Bayer-format sensors can be thought of as “non-square”), so saying a pixel is a certain size, as a general measure across implementations, doesn’t really make sense. In iOS and MacOS, we use “display units,” which can be pixels, or groups of pixels. The ratio usually changes, from device to device.

Y-bar 1y ago
This is my favourite single-pixel interface: https://en.wikipedia.org/wiki/Trafficators https://en.wikipedia.org/wiki/Trafficators
- ChrisMarshallNY 1y ago
  They are sort of coming back, as side-mirror indicators.

ivan_gammel 1y ago

So, the author answers the question: > That means the pixel is a dimensionless unit that is just another name for 1, kind of like how the radian is length divided by length so it also equals one, and the steradian is area divided by area which also equals one. But then for some reason decides to ignore it. I don’t understand this article. Yes, pixels are dimensionless units used for counting, not measuring. Their shape and internal structure is irrelevant (even subpixel rendering doesn’t actually deal with fractions - it alters neighbors to produce the effect).

blenderob 1y ago

The article starts out with an assertion right in the title and does not do enough to justify it. The title is just wrong. Saying pixels are like metres is like saying metres are like apples. When you multiply 3 meter by 4 meter, you do not get 12 meters. You get 12 meter squared. Because "meter" is not a discrete object. It's a measurement. When you have points A, B, C. And you create 3 new "copies" of those points (by geometric manipulation like translating or rotating vectors to those points), you now have 12 points: A, B, C, A1, B1, C1, A2, B2, C2, A3, B3, C3. You don't get "12 points squared". (What would that even mean?) Because points are discrete objects. When you have 3 apples in a row and you add 3 more such rows, you get 4 rows of 3 apples each. You now have 12 apples. You don't have "12 apples squared". Because apples are discrete objects. When you have 3 pixels in a row and you add 3 more such rows of pixels, you get 4 rows of 3 pixels each. You now have 12 pixels. You don't get "12 pixels squared". Because pixels are discrete objects. Pixels are like points and apples. Pixels are not like metres.

Izkata 1y ago
> When you multiply 3 meter by 4 meter, you do not get 12 meters. You get 12 meter squared. "12 meter(s) squared" sounds like a square that is 12 meters on each side. On the other hand, "12 square meters" avoids this weirdness by sounding like 12 squares that are one meter on each side, which the area you're actually describing.
- chii 1y ago
  that's just a quirk of the language. If you use formal notation, 12 m^2 is very clear. But i have yet to see anyone write 12px^2
  - Izkata 1y ago
    It's one that really bothers me because of the unnecessary confusion it adds. As for the rest, see GGP's argument. px^2 doesn't make logical sense. When people are use pixels as length, it's in the same way as "I live 2 houses over" - taking a 2D or 3D object and using one of its dimensions as length/distance.

tomhow 1y ago

See also: A Pixel Is Not a Little Square (1995) [pdf] – http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf

glitchc 1y ago
This is written from a rather narrow perspective (of signal processing) and is clearly wrong in other contexts. For an image sensor designer, gate length, photosensitive area and pixel pitch are all real-valued measurements. That pixels are laid out on a grid simply reflects the ease of constructing electronic circuits this way. Alternative arrangements are possible, Sigma's depth pixels being one commercial example.
- grandempire 1y ago
  Ok, but that’s not what an digital image is. Images are designed to be invariant across camera capture and display hardware. The panel driver should interpret the dsp representation into an appropriate electronic pixel output.
  - fluoridation 1y ago
    Well, "what a digital image is" is a sequence of numbers. There's no single correct way to interpret the numbers, it depends on what you want to accomplish. If your digital image is a representation of, say, the dead components in an array of sensors, the signal processing theoretic interpretation of samples may not be useful as far as figuring out which sensors you should replace.
    - grandempire 1y ago
      > There's no single correct way to interpret the numbers They are just bits in a computer. But there is a correct way of to interpret them in a particular context. For example 32 bits can be meaningless - or it can have an interpretation as a twos complement integer which is well defined. If you are looking to understand how an operating system will display images, or how graphics drivers work, or how photoshop will edit them, or what digital cameras produce, then it’s the point sample definition.

dullcrisp 1y ago

Wait till they hear about fluid ounces.

jrvieira 1y ago

The author is very confused.

gilgoomesh 1y ago

A pixel is two dimensional, by definition. It is a unit of area. Even in the signal processing "sampling" definition of a pixel, it still has an areal density an is therefore still two-dimensional. The problem in this article is it incorrectly assumes a pixel to be a length and then makes nonsensical statements. The correct way to interpret "1920 pixels wide" is "the same width as 1920 pixels arranged in a 1920 by 1 row". In the same way that "square feet" means "feet^2" as "square" acts as a square operator on "feet", in "pixels wide" the word "wide" acts as a square root operator on the area and means "pixels^(-2)" (which doesn't otherwise have a name).

danbruc 1y ago
It is neither a unit of length nor area, it is just a count, a pixel - ignoring the CSS pixel - has no inherent length or area. To get from the number of pixels to a length or area, you need the pixel density. 1920 pixel divided by 300 pixel per inch gives you the length of 6.4 inch and it all is dimensionally consistent. The same for 18 mega pixel, with a density of 300 times 300 pixel per square inch you get an image area of 200 square inch. Here pixel per inch times pixel per inch becomes pixel per square inch, not square pixel per square inch.
- deleted 1y ago
  [deleted]
jillesvangurp 1y ago
CSS got it right by making pixels a relative unit. Meters are absolute. You cannot express pixels in meters. Because they are relative units. If you have a high resolution screen the a CSS pixel is typically be 4 actual display pixels (2x2) instead of just 1. And if you change the zoom level, the amount of display pixels might actually change in fractional ways. The unit only makes sense in relation to what's around it. If you render vector graphics or fonts, pixels are used as relative units. On a high resolution screen it will actually use those extra display pixels. If you want to show something that's exactly 5cm on a laptop or phone screen, you need to know the dimensions of the screen and figure out how many pixels you need per cm to scale things correctly. Css has some absolute units but they only work as expected for print media typically.

bitwize 1y ago

Pixels are not measurement units. They're samples of an image taken a certain distance apart. It's like eggs in a carton: it's perfectly legitimate to say that a carton is 6 eggs long and 3 eggs wide, and holds a total of 18 eggs, because eggs are counted, they're not a length measure except in the crudest sense.

otikik 1y ago

Well the way I see them I don't think they are a unit at all. And the end pixels are "physical things". Like ceramic tiles on a bathroom wall. Your wall might be however many meters in length and you might need however squared meters of tile in order to cover it. But still, if you need 10 tiles high and 20 tiles width, you need 200 tiles to cover it. No tension there. Now you might argue that pixels in a scaled game don't correspond with physical objects in the screen any more. That's ok. A picture of the bathroom wall will look smaller than the wall itself. Or bigger, if you hold it next to your face. It's still 10x20=200 tiles.

fennecbutt 1y ago

Or perhaps it's multivariate and there's no point in trying to squish all the nuance into a single solid definition.

RedNifre 1y ago

What a perplexing article. Isn't a pixel clearly specified as a picture element? Isn't the usage as a length unit just as colloquial as "It's five cars long", which is just a simplified way of saying "It is as long as the length of a car times five", where "car" and "length of car" are very clearly completely separate things? > The other awkward approach is to insist that the pixel is a unit of length Please don't. If you want a unit of length that works well with pixels, you can use Android's "dp" concept instead, which are "density independent pixels" (kinda a bad name if you think about it) and are indeed a unit of length, namely 1dp = 158.75 micro meter, so that you have 160 dp to the inch. Then you can say "It's 10dp by 5dp, so 50 square dp in area.".

tshaddox 1y ago
Yeah, this isn't really that complicated. It's just colloquial usage, not rigorous dimensional analysis. Roughly no one is actually confused by either usage ("1920 by 1080" or "12 megapixels"). It's nearly identical to North American usage of "block" (as in "city block"). Merriam Webster lists these two definitions (among many others): > 6 a (1): a usually rectangular space (as in a city) enclosed by streets and occupied by or intended for buildings > 6 a (2): the distance along one of the sides of such a block
munk-a 1y ago
Another colloquial saying to back this up is that "Oh, that house is five acres down the road" or, for a non-standard unit, "The store is three blocks away". We often use area measurements for length if it's convenient. The pixel is a unit of area - we just occasionally use units of area to measure length.
- JadeNB 1y ago
  > Another colloquial saying to back this up is that "Oh, that house is five acres down the road" or, for a non-standard unit, "The store is three blocks away". We often use area measurements for length if it's convenient. I have never heard someone use the first instance, and I wouldn't understand what it meant. I mean, I could buy that it meant that there is a five-acre plot between that house and where we are now, but it wouldn't give me any useful idea of how far the house is other than "not too close." Perhaps you have in mind that, since the "width" of an acre is a furlong, a house 5 acres away is 5 furlongs away?

rbanffy 1y ago

For those who programmed 8-bit computers or worked with analog video, a pixel is also a unit of time. An image is a long line with some interruptions.

deleted 1y ago

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jmull 1y ago

Hopefully most people get that the exact meaning of "pixel" depends on context? It certainly doesn't make sense to mix different meanings in a mathematical sense. E.g., when referring to a width in pixels, the unit is pixel widths. We shorten it and just say pixels because it's awkward and redundant to say something like "the screen has a width of 1280 pixel widths", and the meaning is clear to the great majority of readers.

_wire_ 1y ago

This article wastes readers' time by pretending to command of a subject in a manner that is authoritative only in its uncertainty. Pixel is an abbreviation for 'picture element' which describes a unit of electronic image representation. To understand it, consider picture elements in the following context... (Insert X different ways of thinking about pictures and their elements.) If there is a need for a jargon of mathematical "dimensionality" for any of these ways of thinking, please discuss it in such context. Next up: <i>A musical note is a unit of...</i>

scotty79 1y ago

Pixel is just contextual. When you are talking about one dimensional things it's a unit of length. In all mother cases it's a unit of area.

teknopaul 1y ago

The pixel ain't no problem. A "megapixel" is simply defined as 1024 pixels squared ish. There is no kilopixel. Or exapixel. No-one doesn't understand this?

webstrand 1y ago

This kind of thing is common in english, though. "an aircraft carrier is 3.5 football fields long" The critical distinction is the inclusion of a length dimension in the measurement: "1920 pixels wide", "3 mount everests tall", "3.5 football fields long", etc.

jefftk 1y ago

This isn't just pixels, it's the normal way we use rectangular units in common speech: * A small city might be ten blocks by eight blocks, and we could also say the whole city is eighty blocks. * A room might by 13 tiles by 15 tiles, or 295 tiles total. * On graph paper you can draw a rectangle that's three squares by five squares, or 15 squares total.

tuzemec 1y ago

Also a measurement of life. Back in the 320x200 game days, when playing something with a health bar, we used to joke that someone had one pixel of life left when near death.

alzamixer 1y ago

Should be pixel as area and pixel-length as 1-dimensional unit. So an image could be 1 mega pixel, or 1000 times 1000 pixel-lengths.

nout 1y ago

Pixel is also a unit of a phone.

kazinator 1y ago

A bathroom tile is also a unit of length and area. A wall can be so many tiles high by so many wide, and its area the product, also measured in tiles. It is just word semantics revolving around a synecdoche. When we say that an image is 1920 pixels wide, the precise meaning is that it is 1920 times the width of a pixel. Similarly 1024 pixels high means 1024 times the height of a pixel. The pixel is not a unit of length; its height or width are (and they are different when the aspect ratio is not 1:1!) A syntax-abbreviating semantic device in human language where part of something refers to the whole or vice versa is called a synecdoche. Under synecdoche, "pixel" (the whole) can refer to "pixel width" (part or property of the whole). Just like the synecdoche "New York beats Chicago 4:2" refer to basketball teams in its proper context, not literally the cities.

dusted 1y ago

I think the author forgets that pixels inherently have both width and height, a single pixel, is inherently a 2 dimensional entity, whereas the meter is a purely one dimensional concept. You don't usually talk about whether your meters are the same height as they are tall, or whether they're taller than they're wide.. because they don't have those two dimensions.. You don't talk about how your centimeters are arranged within your meter either.. (you can talk about how your subpixels are, and even if there are 3 or 4 of them). So, I don't think it's entirely valid to talk about pixels as if they are pure, one dimensional units.. They're _things_ and you can talk about how many things wide or tall something is, and you can talk about how many things something has. Very much the same way you can with bricks (which are mostly never square) (though tiles are, you never talk about how many kilotiles is in your bathroom either, yet you can easily talk about how many tiles wide or tall a wall is). So, no, pixels is not a unit in the mathematical sense.. it's an item, in the physical sense. There are also things like scanners, that may have only one row of pixels on the scanner sensor, it does not have an area of zero, and you don't need to specify that there's one pixel on the other axis, because it's an inherent property of pixels that they have both width and height and thus area in and of themselves.