[HN Gopher] Pixel is a unit of length and area
       ___________________________________________________________________
        
       Pixel is a unit of length and area
        
       Author : anitil
       Score  : 120 points
       Date   : 2025-04-23 07:20 UTC (15 hours ago)
        
 (HTM) web link (www.nayuki.io)
 (TXT) w3m dump (www.nayuki.io)
        
       | anitil wrote:
       | This is a fun post by Nayuki - I'd never given this much thought,
       | but this takes the premise and runs with it
        
       | knallfrosch wrote:
       | 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 wrote:
         | City blocks, too.
        
           | Aldipower wrote:
           | In the US...
        
             | jeltz wrote:
             | 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 wrote:
             | 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 wrote:
               | 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 wrote:
               | 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 wrote:
         | Not all pixels are square, though! Does anyone remember
         | anamorphic DVDs?
         | https://en.wikipedia.org/wiki/Anamorphic_widescreen
        
           | nayuki wrote:
           | Never mind anamorphic DVDs, all of them use non-square
           | pixels. The resolution of DVD is 720x480 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 wrote:
       | Reminds me of this Numberphile w/ Cliff Stoll [1]: The Nescafe
       | Equation (43 coffee beans)
       | 
       | [1] https://youtu.be/3V84Bi-mzQM
        
       | surfingdino wrote:
       | 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 wrote:
         | Is a pixel not a pixel when it's in a different color space?
         | (HSV, XYZ etc?)
        
           | surfingdino wrote:
           | RGB is the most common colour space, but yes, other colour
           | spaces are available.
        
         | echoangle wrote:
         | And what's the difference between a photosite and a pixel?
         | Sounds like a difference made up to correct other people.
        
           | surfingdino wrote:
           | 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.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 wrote:
             | 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.
        
               | surfingdino wrote:
               | You are right about the differences in the number of
               | sensors, there may be more. I prefer to talk about
               | photosites, because additional properties like photosite
               | size or sensor photosite density help me make better
               | decisions when I'm selecting cameras/sensors for a photo
               | project. For example, a 24MP M43 sensor is not the same
               | as a 24MP APS-C or FF sensor, even though the image files
               | they produce have the same number of pixels. Similarly, a
               | 36MP FF sensor is essentially the same a 24MP APS-C
               | sensor, it produces image files that contain more pixels
               | from a wider field of view, but the resolution of the
               | sensor stays the same, because both sensors have the same
               | photosite density (if you pair the same lens with both
               | sensors).
        
             | anfractuosity wrote:
             | I didn't think a single photosite was directly converted to
             | a single pixel, there's quite a number of different
             | demosaicing algorithms.
             | 
             | Edit: Upon doing some more reading it sounds like a
             | photosite or sensel, isn't a group of sensors, but a single
             | sensor, which can pick up r,g,b,.. light - "each individual
             | photosite, remember, records only one colour - red, green
             | or blue" - https://www.canon-europe.com/pro/infobank/image-
             | sensors-expl...
             | 
             | I couldn't seem to find a particular name for the RGGB/..
             | pattern that a bayer filter consists of an array of.
        
       | Sharlin wrote:
       | 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 wrote:
         | Digital photography then takes us on to subpixels, Bayer
         | filters (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 wrote:
       | 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 wrote:
         | > "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."
        
         | nayuki wrote:
         | 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 wrote:
       | 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.
        
         | gnfargbl wrote:
         | Exactly. Pixels are indivisible quanta, not units of any kind
         | of distance. Saying pixel^2 makes as much sense as counting the
         | number of atoms on the surface of a metal and calling it
         | atoms^2.
        
           | chii wrote:
           | So how does subpixels come into play under this idea of
           | quanta?
        
             | n0n0n4t0r wrote:
             | I think we'll need to use some maths from qcd lattice !
        
             | masklinn wrote:
             | Quarks? They're sub-units of hadrons but iirc they can't be
             | found on their own.
        
             | starkparker wrote:
             | Pixels then become containers and subpixels become
             | quantfiable entities within each pixel. In the apple
             | analogy, each crate contains three countable apples and you
             | can count both the crates and the apples independently.
             | 
             | This idea itself breaks down when we get to triangular
             | subpixel rendering, which spans pixels and divides
             | subpixels. But it's also a minor form of optical illusion,
             | so making sense of it is inherently fraught.
             | 
             | Maybe a pixel is just a pixel.
        
         | petesergeant wrote:
         | 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 wrote:
           | 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 wrote:
             | What's the standard size of a city block, the other
             | countable example given by the original author?
        
               | jeltz wrote:
               | 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 wrote:
             | Pixel counts generally represent areas by taking the number
             | of pixels inside a region of the plane, but they can
             | represent lengths by taking the number of pixels inside a
             | certain extent of a single line or column of the grid: it
             | is, actually, a thin rectangle.
        
             | vikingerik wrote:
             | Football fields also have the fun property of varying in
             | the _third_ dimension. They 're built with a crown in the
             | middle so that water will drain off towards the edges, and
             | that can vary significantly between instances.
             | 
             | And pixels are even starting to vary in the third dimension
             | too, with the various curved and bendable and foldable
             | displays.
        
               | robotresearcher wrote:
               | Pixels used to be realized non-flat in the CRT days.
        
           | timerol wrote:
           | This example illustrates potential confusion around non-
           | square pixels. 5 football fields long makes perfect sense,
           | but I'm not sure if 2 football fields wide means "twice the
           | width of a football field" or "width equaling twice the
           | length of a football field". I would lean towards the latter
           | in colloquial usage, which means that the area is definitely
           | not the same as the area of 10 football fields
        
             | pests wrote:
             | I would lean towards the former. I really don't think
             | people are trying to compare the width to the length when
             | discussing football fields casually.
             | 
             | If I told you parking spots are about two bowling lane's
             | wide... I'm obviously not trying to say they are 120ft
             | wide.
        
               | thfuran wrote:
               | I don't think that's obvious at all if thisy talking
               | about the length and the width and not describing
               | something I know to be much smaller in any dimension than
               | the length of a lane.
        
         | solardev wrote:
         | > If I have a bin of apples, and I say it's 5 apples wide, and
         | 4 apples tall
         | 
         | ...then you have a terrible bin for apple storage and should
         | consider investing in a basket ;)
        
           | pphysch wrote:
           | If you don't care about bruising
        
         | _ph_ wrote:
         | That is exactly how it is and it makes the whole article
         | completely pointless. Especially as the article in the second
         | sentence correctly writes "1920 pixels wide".
        
         | GuB-42 wrote:
         | It think the point of the article is that you don't say "5
         | pixels wide x 4 pixels tall" but just "5 pixels x 4 pixels",
         | though I would say that "5x4 pixels" is the most common and
         | most correct terminology.
         | 
         | And the article concludes with : "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". Which matches your conclusion.
        
       | ttoinou wrote:
       | 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 wrote:
       | 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 wrote:
         | It's not a unit of information. How many bytes does a 320x240
         | image take? You don't know until you specify the pixel bit
         | depth in bpp (bits per pixel).
        
       | justin_ wrote:
       | > 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
        
         | toxik wrote:
         | 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 wrote:
         | 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 wrote:
           | DACs do a zero-order hold, which is equivalent to a pixel as
           | a square.
        
           | toxik wrote:
           | The representation of pixels on the screen is not necessarily
           | normative for the definition of the pixel. Indeed, since
           | different display devices use different representations as
           | you point out, it can't really be. You have to look at the
           | source of the information. Is it a hit mask for a game? Then
           | they are squares. Is it a heatmap of some analytical
           | function? Then they are points. And so on.
        
           | justin_ wrote:
           | > A camera does not take point sample snapshots, it
           | integrates lightfall over little rectangular areas.
           | 
           | Integrates this information into what? :)
           | 
           | > A modern display does not reconstruct an image the way a
           | DAC reconstructs sounds
           | 
           | Sure, but some software may apply resampling over the
           | original signal for the purposes of upscaling, for example.
           | "Pixels as samples" makes more sense in that context.
           | 
           | > It is pretty reasonable in the modern day to say that an
           | idealized pixel is a little square.
           | 
           | I do agree with this actually. A "pixel" in popular
           | terminology is a rectangular subdivision of an image, leading
           | us right back to TFA. The term "pixel art" makes sense with
           | this definition.
           | 
           | Perhaps we need better names for these things. Is the "pixel"
           | the name for the sample, or is it the name of the square-ish
           | thing that you reconstruct from image data when you're ready
           | to send to a display?
        
             | echoangle wrote:
             | > Integrates this information into what? :)
             | 
             | Into electric charge? I don't understand the question, and
             | it sounds like the question is supposed to lead readers
             | somewhere.
             | 
             | The camera integrates incoming light into a tiny square
             | into an electric charge and then reads out the charge (at
             | least for a CCD), giving a brightness (and with the Bayer
             | filter in front of the sensor, a color) for the pixel. So
             | it's a measurement over the tiny square, not a point
             | sample.
        
               | justin_ wrote:
               | > The camera integrates incoming light into a tiny square
               | [...] giving a brightness (and with the Bayer filter in
               | front of the sensor, a color) for the pixel
               | 
               | This is where I was trying to go. The pixel, the result
               | at the end of all that, is the single value (which may be
               | a color with multiple components, sure). The physical
               | reality of the sensor having an area and generating a
               | charge is not relevant to the signal processing that
               | happens after that. For Smith, he's saying that this
               | sample is best understood as a point, rather than a
               | rectangle. This makes more sense for Smith, who was
               | working in image processing within software, unrelated to
               | displays and sensors.
        
               | echoangle wrote:
               | It's a single value, but it's an integral over the
               | square, not a point sample. If a shine a perfectly
               | focused laser very close to the corner of one sensor
               | pixel, I'll still get a brightness value for the pixel.
               | If it were a point sample, only the brightness at a
               | single point would give an output.
               | 
               | And depending on your application, you absolutely need to
               | account for sensor properties like pixel pitch and color
               | filter array. It affects moire pattern behavior and
               | creates some artifacts.
               | 
               | I'm not saying you can't think of a pixel as a point
               | sample, but correcting other people who say it's a little
               | square is just wrong.
        
               | grandempire wrote:
               | > It affects moire pattern behavior and creates some
               | artifacts.
               | 
               | Yes. The spacing between point samples determines the
               | frequency, a fundamental characteristic of a dsp signal.
        
               | glitchc wrote:
               | It's never a point source. Light is integrated over a
               | finite area to form a singke color sample. During Bayer
               | mosaicking, contributions from neighbouring pixels are
               | integrated to form samples of complementary color
               | channels.
        
               | justin_ wrote:
               | > Light is integrated over a finite area to form a singke
               | color sample. During Bayer mosaicking, contributions from
               | neighbouring pixels are integrated to form samples of
               | complementary color channels.
               | 
               | Integrated into a single color sample indeed. After all
               | the integration, mosaicking, and filtering, a single
               | sample is calculated. That's the pixel. I think that's
               | where the confusion is coming from. To Smith, the "pixel"
               | is the sample that lives in the computer.
               | 
               | The actual realization of the image sensors and their
               | filters are not encoded in a typical image format, nor
               | used in a typical _high level_ image processing
               | pipelines. For abstract representations of images, the
               | "pixel" abstraction is used.
               | 
               | The initial reply to this chain focused on how camera
               | sensors capture information about light, and yes, those
               | sensors take up space and operate over time. But the
               | pixel, the piece of data in the computer, is just a point
               | among many.
        
               | glitchc wrote:
               | > Integrated into a single color sample indeed. After all
               | the integration, mosaicking, and filtering, a single
               | sample is calculated. That's the pixel. I think that's
               | where the confusion is coming from. To Smith, the "pixel"
               | is the sample that lives in the computer.
               | 
               | > But the pixel, the piece of data in the computer, is
               | just a point among many.
               | 
               | Sure, but saying that this is _the_ pixel, and negating
               | all other forms as not  "true" pixels is arbitrary. The
               | real-valued physical pixels (including printer dots) are
               | equally valid forms of pixels. If anything, it would be
               | impossible for humans to sense the pixels without
               | interacting with the real-valued forms.
        
               | SAI_Peregrinus wrote:
               | IMO Smith misapplied the term "pixel" to mean "sample". A
               | pixel is a physical object, a sample is a logical value
               | that corresponds in some way to the state of the physical
               | object (either as an input from a sensor pixel or an
               | output to a display pixel) but is also used in signal
               | processing. Samples aren't squares, pixels (usually) are.
        
           | jeremyscanvic wrote:
           | A slightly tangential comment: integrating a continuous image
           | on squares paving the image plane might be best viewed as
           | applying a box filter to the continuous image, resulting in
           | another continuous image, then sampling it point-wise at the
           | center of each square.
           | 
           | It turns out that when you view things that way, pixels as
           | points continues to make sense.
        
         | creeble wrote:
         | The 'point' of Alvy's article is that pixels should be treated
         | as point sources when manipulating them, not when displaying
         | them.
         | 
         | Obviously, when a pile of pixels is shown on a screen (or for
         | that matter, collected from a camera's CCD, or blobbed by ink
         | on a piece of paper), it will have some shape: The shape of the
         | LCD matrix, the shape of the physical sensor, the shape of the
         | ink blot. But those aren't pixels, they're the physical shapes
         | of the pixels expressed on some physical medium.
         | 
         | If you're going to manipulate pixels in a computer's memory
         | (like by creating more of them, or fewer), then you'd do best
         | by treating the pixels as sampling points - at this point, the
         | operation is 100% sampling theory, not geometry.
         | 
         | When you're done, and have an XY matrix of pixels again, you'll
         | no doubt have done it so that you can give those pixels _shape_
         | by displaying them on a screen or sheet of paper or some other
         | medium.
        
       | Aldipower wrote:
       | A Pixel is a telephone.
        
       | JimDabell wrote:
       | This depends upon who you ask. CSS defines a pixel as an angle:
       | 
       | https://www.w3.org/TR/css-values-3/#reference-pixel
        
         | didroe wrote:
         | That's the definition of a "reference pixel", not a pixel. They
         | actually refer to a pixel (and the angle) in the definition.
        
       | ChrisMarshallNY wrote:
       | 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 wrote:
         | This is my favourite single-pixel interface:
         | https://en.wikipedia.org/wiki/Trafficators
        
           | ChrisMarshallNY wrote:
           | They are sort of coming back, as side-mirror indicators.
        
       | ivan_gammel wrote:
       | 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 wrote:
       | 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 wrote:
         | > 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 wrote:
           | 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 wrote:
             | 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 wrote:
       | See also:
       | 
       | A Pixel Is Not a Little Square (1995) [pdf] -
       | http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf
        
         | glitchc wrote:
         | 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 wrote:
           | 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 wrote:
             | 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 wrote:
               | > 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.
        
               | Dylan16807 wrote:
               | Cameras don't take point samples. That's an
               | approximation, just as inaccurate as a rectangle
               | approximation.
               | 
               | And for pixel art, the intent is usually far from points
               | on a smooth color territory.
               | 
               | Multiple interpretations matter within different contexts
               | inside the computer context.
        
               | grandempire wrote:
               | > Cameras don't take point samples. That's an
               | approximation
               | 
               | They use a physical process to attempt to determine light
               | at a single point. That's their model they try to
               | approximate.
               | 
               | > And for pixel art, the intent is usually far from
               | points on a smooth color territory.
               | 
               | And notice that to display pixel art you need to tell it
               | to interpret the image data differently.
               | 
               | Also it has a vastly different appearance on a CRT where
               | it was designed which is less like a rectangle.
        
             | glitchc wrote:
             | Yeah but the article is about a pixel, which has different
             | meanings. Making blanket statements is not helpful in
             | resolving definitions.
             | 
             | Truth is, a pixel is both a sample and a transducer. And in
             | transduction, a pixel is both an integrator and an emitter.
        
               | grandempire wrote:
               | I'll quote my other comment:
               | 
               | > If you are looking to understand how your operating
               | system will display images, or how your graphics drivers
               | work, or how photoshop will edit them, or what digital
               | cameras aim to produce, then it's the point sample
               | definition.
        
               | tobr wrote:
               | Sometimes yes. Sometimes no! There are certainly
               | situations where a pixel will be scaled, displayed,
               | edited or otherwise treated as a little square.
        
               | seba_dos1 wrote:
               | A little rectangle even.
        
               | grandempire wrote:
               | What is a little rectangle? Physical display pixels are
               | separate RGB leds with a non-rectangular shape.
        
               | Dylan16807 wrote:
               | They're rectangles on my monitor.
        
               | cma wrote:
               | If black and white or some other cases, but there are
               | typically subpixels that can make things like sparse
               | enough text stroke transitions get 3X horizontal
               | resolution.
        
               | Dylan16807 wrote:
               | The subpixels are rectangles on most screens.
        
               | grandempire wrote:
               | They tend to have rounded or cut corners and are not
               | uniform.
        
               | grandempire wrote:
               | Do the 3 separate sub pixels look like a photoshop pixel?
        
               | Dylan16807 wrote:
               | I'm not sure what you mean by Photoshop pixel.
               | 
               | They also look more like a square when I back away. And
               | the mismatch of the square model doesn't mean the point
               | model is good.
        
               | afandian wrote:
               | BBC Micro in graphics mode 2 the pixel is a 2:1
               | rectangle. Other geometries for different modes. It's
               | going back a bit, but very much living memory!
               | 
               | https://beebwiki.mdfs.net/MODE_2
        
             | kjkjadksj wrote:
             | Well the camera sensor captures a greater dynamic range
             | than the display or print media or perhaps even your eyes,
             | so something has to give. If you ever worked with a linear
             | file without gamma correction you will understand what I
             | mean.
        
               | grandempire wrote:
               | And that full dynamic range is in the images's point
               | samples, ready to be remapped for a physical output.
        
         | calibas wrote:
         | If you want a good example of what happens when you treat
         | pixels like they're just little squares, disable font
         | smoothing. Anti-aliasing, fonts that look good, and smooth
         | animation are all dependent upon subpixel rending.
         | 
         | https://en.wikipedia.org/wiki/Subpixel_rendering
         | 
         |  _Edit_ : For the record, I'm on Win 10 with a 1440p monitor
         | and disabling font smoothing makes a very noticeable
         | difference.
         | 
         | People are acting like this is some issue that no longer
         | exists, and you don't have to be concerned with subpixel
         | rendering anymore. That's not true, and highlights a bias
         | that's very prevalent here on HN. Just because I have a fancy
         | retina display doesn't mean the average user does. If you
         | pretend like subpixel rendering is no longer a concern, you can
         | run into situations where fonts look great on your end, but an
         | ugly jagged mess for your average user.
         | 
         | And you can tell who the Apple users are because they believe
         | all this went away years ago.
        
           | kccqzy wrote:
           | This might have been a good example fifteen years ago. These
           | days with high-DPI displays you can't perceive a difference
           | between font smoothing being turned on and off. On macOS for
           | example font smoothing adds some faux bold to the fonts, and
           | it's long been recommended to turn it off. See for example
           | the influential article https://tonsky.me/blog/monitors/
           | which explains that font smoothing used to do subpixel
           | antialiasing, but the whole feature was removed in 2018. It
           | also explains that this checkbox doesn't even control regular
           | grayscale antialiasing, and I'm guessing it's because
           | downscaling a rendered @2x framebuffer down to the physical
           | resolution inherently introduces antialiasing.
        
             | calibas wrote:
             | Maybe true for Mac users, but the average Win 10 desktop is
             | still using a 1080p monitor.
        
               | hulium wrote:
               | The users may have 1080p monitors, but even Windows does
               | not do subpixel antialiasing in its new apps (UWP/WinUI)
               | anymore. On Linux, GTK4 does not do subpixel antialiasing
               | anymore.
               | 
               | The reason is mostly that it is too hard to make it work
               | under transformations and compositing, while higher
               | resolution screens are a better solution for anyone who
               | cares enough.
        
               | calibas wrote:
               | > even Windows does not do subpixel antialiasing in its
               | new apps (UWP/WinUI) anymore
               | 
               | This is a little misleading, as the new versions of Edge
               | and Windows Terminal do use subpixel antialiasing.
               | 
               | What Microsoft did was remove the feature on a system
               | level, and leave implementation up to individual apps.
        
               | verall wrote:
               | Is this why font rendering on my Win11 laptop looks like
               | shit on my 1440p external monitor?
               | 
               | Laptop screen is 4k with 200% scaling.
               | 
               | Seriously the font rendering in certain areas (i.e.
               | windows notification panel) is actually dogshit. If I
               | turn off the 200% scaling on the laptop screen then
               | reboot it looks correct again.
        
           | wat10000 wrote:
           | I don't think that's true anymore. Modern high-resolution
           | displays have pixels small enough that they don't really
           | benefit from sub-pixel rendering, and logical pixels have
           | become decoupled from physical pixels to the point of making
           | sub-pixel rendering a lot more difficult.
        
             | 7jjjjjjj wrote:
             | It's still true for everyone who doesn't have a high DPI
             | monitor. We're talking about a feature that doubles the
             | price of the display for little practical value. It's not
             | universal, and won't be for a long time.
        
           | dahart wrote:
           | You're conflating different topics. LCD subpixel rendering
           | and font smoothing is often implemented by treating the
           | subpixels as little rectangles, which is the same mistake as
           | treating pixels as squares.
           | 
           | Anti-aliasing can be and is done on squares routinely. It's
           | called 'greyscale antialiasing' to differentiate from LCD
           | subpixel antialiasing, but the name is confusing since it
           | works and is most often used on colors.
           | 
           | The problem Alvy-Ray is talking about is far more subtle. You
           | can do anti-aliasing with little squares, but the result
           | isn't 100% correct and is not the best result possible no
           | matter how many samples you take. What he's really referring
           | to is what signal processing people call a box filter, versus
           | something better like a sinc or Gaussian or Mitchell filter.
           | 
           | Regarding your edit, on a high DPI display there's very
           | little practical difference bewteen LCD subpixel antialiasing
           | and 'greyscale' (color) antialiasing. You don't need LCD
           | subpixels to get effective antialiasing, and you can get
           | mostly effective antialiasing with square shaped pixels.
        
             | calibas wrote:
             | We're going off on tangents here, I only brought this up to
             | reinforce the idea that a pixel is not a little square.
             | 
             | And I guess I should have explicitly stated that I'm not
             | talking about high-DPI displays, subpixel rendering
             | obviously doesn't do much good there!
             | 
             | My point is simply this, if you don't treat pixel like
             | discrete little boxes that display a single color, you can
             | use subpixels to effectively increase the resolution on
             | low-DPI monitors. Yes, you can use greyscale antialiasing
             | instead, you will even get better performance, but the
             | visual quality will suffer on your standard desktop PC
             | monitor.
        
         | nayuki wrote:
         | Agreed. The fact that a pixel is an infinitely small point
         | sample - and not a square with area - is something that Monty
         | explained in his demo too: https://youtu.be/cIQ9IXSUzuM?t=484
        
           | dahart wrote:
           | Eh, calling it infinitely small is at least as misleading as
           | calling it a square. While they are both mostly correct,
           | neither Monty's explanation nor Alvy-Rays are all that good.
           | Pixels are samples taken at a specific point, but pixel
           | values do represent area one way or another. Often they are
           | not squares, but on the other hand LCD pixels are pretty
           | square-ish. Camera pixels are integrals over the sensor area,
           | which captures an integral over a solid angle. Pixels don't
           | have a standard shape, it depends on what capture or display
           | device we're talking about, but no physical capture or
           | display devices have infinitely small elements.
        
             | kjkjadksj wrote:
             | Some early variants of sony a7 had fewer but larger pixels
             | to improve light gathering at high iso.
        
             | wtallis wrote:
             | Camera pixels represent an area, but pixels coming out of a
             | 3D game engine usually represent a point sample. Hand-drawn
             | 2d pixel art is explicitly treating pixels as squares. All
             | of these are valid uses that must coexist on the same
             | computer.
        
           | jansan wrote:
           | Signal processing engineers against the rest of the world.
        
           | kazinator wrote:
           | A pixel is not the sample(s) that is value came from. Given a
           | pixel (of image data) you don't know what samples are behind
           | it. It could have been point-sampled with some optical sensor
           | far smaller than the pixel (but not infinitely small,
           | obviously). Or it could have been sampled with a gaussian
           | bell shaped filter a bit wider than the pixel.
           | 
           | A 100x100 thumbnail that was reduced from a 1000x1000 image
           | might have pixels which are derived from 100 samples of the
           | original image (e.g. a simple average of a 10x10 pixel
           | block). Or other possibilities.
           | 
           | As an _abstraction_ , a pixel definitely doesn't represent a
           | point sample, let alone an infinitely small one. (There could
           | be some special context in which it does but not as a
           | generality.)
        
       | dullcrisp wrote:
       | Wait till they hear about fluid ounces.
        
       | jrvieira wrote:
       | The author is very confused.
        
       | gilgoomesh wrote:
       | 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 wrote:
         | 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.
        
         | jillesvangurp wrote:
         | 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.
        
         | bnegreve wrote:
         | > in "pixels wide" the word "wide" acts as a square root
         | operator on the area and means "pixels^(-2)"
         | 
         | Did you meant "pixels^(1/2)"? I'm not sure what kind of units
         | pixels^(-2) would be.
        
           | nayuki wrote:
           | pixel^(-2) is "per squared pixel". Analogously, 1 pascal = 1
           | newton / 1 metre^2. (Pressure is force per squared length.)
        
         | grandempire wrote:
         | > A pixel is two dimensional, by definition.
         | 
         | A pixel is a point sample by definition.
        
           | SAI_Peregrinus wrote:
           | An odd definition. A pixel is a physical object, a picture
           | element in a display or sensor. The value of a pixel at a
           | given time is a sample, but the sample isn't the pixel.
        
             | grandempire wrote:
             | Definitions of technical things you aren't familiar with
             | tend to be odd.
             | 
             | You are referring to a physical piece of a display panel. A
             | representation of an image in software is a different
             | thing. Hardware and software transforms the dsp signal of
             | an image into voltages to drive the physical pixel. That
             | process takes into account physical characteristics like
             | dimensions.
             | 
             | Oh btw physical pixels aren't even square and each RGB
             | channel is a separate size and shape.
        
         | chii wrote:
         | > The correct way to interpret "1920 pixels wide" is "the same
         | width as 1920 pixels arranged in a 1920 by 1 row".
         | 
         | But to be contrarian, the digital camera world always markets
         | how many megapixels a camera has. So in essense, there are
         | situations where pixels are assumed to be an area, rather than
         | a single row of X pixels wide.
        
           | SAI_Peregrinus wrote:
           | The digital camera world also advertises the sensor size. So
           | a 24MP APS-C camera has smaller pixels than a 24MP Full-frame
           | camera, for example.
        
         | hinkley wrote:
         | Same as if you were building a sidewalk and you wanted to
         | figure out its dimensions, you'd base it off the size of the
         | pavers. Because half pavers are a pain and there are no half
         | pixels.
        
       | bitwize wrote:
       | 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 wrote:
       | 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 wrote:
       | Or perhaps it's multivariate and there's no point in trying to
       | squish all the nuance into a single solid definition.
        
       | RedNifre wrote:
       | 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 wrote:
         | 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 wrote:
         | 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 wrote:
           | > 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 wrote:
       | 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.
        
       | jmull wrote:
       | 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_ wrote:
       | 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 wrote:
       | 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 wrote:
       | 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 wrote:
       | 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 wrote:
       | 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 wrote:
       | 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 wrote:
       | 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 wrote:
       | Pixel is also a unit of a phone.
        
       | kazinator wrote:
       | 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.
        
       ___________________________________________________________________
       (page generated 2025-04-23 23:01 UTC)