Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A Pixel Is Not A Little Square (1995) [pdf]

alvyray.com

Post reply on HN
Print view View original

21–30 of 81 posts

Re: A Pixel Is Not A Little Square (1995) [pdf]

#21

Post by robbrown451 »

I wrote this on Quora several years ago, answering the questions of why pixels are square (and quickly clarified that I interpreted it as "why are they laid out on a rectangular grid?"): https://www.quora.com/Why-are-computer-pixels-square/answer/...

The more I've thought about it since, the more I think we should represent images with hexagonal pixels (i.e., laid out on a hex grid), and that color images should treat the center points of red, green, and blue subpixels as not being right on top of each other. (the third image in the post shows how they would be arranged, which is actually similar to how they are on some displays)

It would be a little harder to deal with for graphics programmers who are working at a pixel level, or at the least, it would require a bit of relearning. But it makes more sense in so many ways. Hex is just a better way of "circle packing" (as you notice if you arrange a bunch of pennies on a table), and of course real world displays tend to have the red, green and blue subpixels offset from one another anyway. (are there any that don't?)

Obviously it isn't easy to change something like this at this point, but still, I find the idea fascinating, and appealing to the OCD efficiency fan in me.

Re: A Pixel Is Not A Little Square (1995) [pdf]

#23

Post by anderskaseorg »

raphlinus wrote: post #18
anderskaseorg wrote: post #17

Earlier quoted context omitted.

> * What gamma curve yields the perception of equal width of black-on-white and white-on-black thin lines (also relevant for text)? (Hint: likely not linear luminance) Gamma curves do not affect black and white themselves, only intermediate grays. It’s true that grays are usually used to draw antialiased black and white lines, but we can also think about “ideal” (axis-aligned, pixel-centered, non-antialiased) black a…

I should have clarified that I meant lines with subpixel phase and possibly widths that are not integral numbers of pixels, ie the antialiased case. Also I totally agree that we need to take into account the perceptual differences between black-on-white and white-on-black even assuming the display technology is perfect. That's one reason doing these studies is not trivial!

The non-antialiased “case” is one spot among the continuum of antialiased “cases”; it doesn’t satisfy totally different perceptual rules. What gamma curve would you propose to correct for the perceptual equality of a 9.3px white-on-black line with a 11.6px black-on-white line? What I’m saying is that you’re presupposing the wrong layer to make the correction (antialiasing or no).

Re: A Pixel Is Not A Little Square (1995) [pdf]

#24

Post by raphlinus »

anderskaseorg wrote: post #23
raphlinus wrote: post #18

Earlier quoted context omitted.

I should have clarified that I meant lines with subpixel phase and possibly widths that are not integral numbers of pixels, ie the antialiased case. Also I totally agree that we need to take into account the perceptual differences between black-on-white and white-on-black even assuming the display technology is perfect. That's one reason doing these studies is not trivial!

The non-antialiased “case” is one spot among the continuum of antialiased “cases”; it doesn’t satisfy totally different perceptual rules. What gamma curve would you propose to correct for the perceptual equality of a 9.3px white-on-black line with a 11.6px black-on-white line? What I’m saying is that you’re presupposing the wrong layer to make the correction (antialiasing or no).

You are correct. Change my third question to, "after applying a correct gamma curve to achieve perceptually uniform line widths in the unipolar case, what is the correspondence of line widths when inverting the polarity to preserve the perception of width matching?" Then you want to break that down into the contribution assuming a perfect display and the effect from lower dpi.

This question is less important than the other two, and plausibly the best place to address the effect is in design, rather than rendering.

Re: A Pixel Is Not A Little Square (1995) [pdf]

#26

Post by bjourne »

A pixel is a picture element. An element of a picture. Hence the name... It turns out that thinking of them as little boxes arranged in rectangular grids is very useful. Because that is how computers deal with them. Not as point samples.

The article reminds me of the many mathematical text I've read insisting on that vectors are not tuples of numbers. That thinking of them as anything other than directions with magnitudes is wrong. Technically, that might be correct but vectors-as-numbers is much more useful when calculating with them. When you get into more abstract mathematics, and your vectors contain other kinds of algebraic objects, such as polynomials, you are already so accustomed with them that you can think of them as flying burritos if you like.

When I teach graphics programming, I will continue to tell students that pixels are like little boxes.

Re: A Pixel Is Not A Little Square (1995) [pdf]

#27

Post by nothis »

want2know wrote: post #25

The same is true for digital audio. We are so used to see the visual presentation of samples that look like a bar diagram, that a lot of people think analog sounds better because the curves are smoother. Chris Montgomery has a great talk about this.

>We are so used to see the visual presentation of samples that look like a bar diagram, that a lot of people think analog sounds better because the curves are smoother.

Except for a philosophical debate about continuity, isn't that true?

Re: A Pixel Is Not A Little Square (1995) [pdf]

#28

Post by dahart »

BubRoss wrote: post #8
raphlinus wrote: post #3

I imagine this came up partly as a result of the recent alpha compositing discussion. We desperately need some research, based in user studies and using modern display technology, to settle some basic questions: * What reconstruction filter gives the best results? Is it the same for vector (text) and natural images? By "best" I do mean contrast (sharpness) and lack of visible artifacts. * For rendering of very thin l…

I can tell you right now that you will have a very difficult time beating a normalized gauss filter with a diameter of around 2.2 pixels in a general case. Color and luminance is a separate and orthogonal issue from filtering. I also know that people get away with compositing without converting to linear space, but I'm skeptical that any benefits they see aren't just a matter of getting the color curve they want for…

I was working at PDI Dreamworks during one of the semi annual investigations into which filter kernel was best. And I was completely blown away by how quickly the lighting sup could identify and react to various filters. Gaussian was voted down reliably and repeatedly for being too blurry.

Personally, I like the extra blur I get (and extra safety and guarantees) you get with Gaussian. Back in the NTSC days I discovered that vertically blurring interlaced video made it noticeably more clear and visible, even though it was softer.

But, If you do really spend time with sharper filters, it is true that Gaussian is softer and some pros really do want sharper images than Gaussian can provide.

Re: A Pixel Is Not A Little Square (1995) [pdf]

#29

Post by arundelo »

nothis wrote: post #27
want2know wrote: post #25

The same is true for digital audio. We are so used to see the visual presentation of samples that look like a bar diagram, that a lot of people think analog sounds better because the curves are smoother. Chris Montgomery has a great talk about this.

>We are so used to see the visual presentation of samples that look like a bar diagram, that a lot of people think analog sounds better because the curves are smoother. Except for a philosophical debate about continuity, isn't that true?

http://productionadvice.co.uk/no-stair-steps-in-digital-audi...

The “stair-steps” you see in your DAW when you zoom up on a digital waveform only exist inside the computer. [...] When digital audio is played back in the Real World, the reconstruction filter doesn’t reproduce those stair-steps – and the audio becomes truly analogue again.

Re: A Pixel Is Not A Little Square (1995) [pdf]

#30

Post by dahart »

This piece is a classic and a must-read for graphics people, but do remember that this was written before LCD displays. Today’s pixels actually are little squares to a much greater degree than CRTs in 1995. That doesn’t change the theory or truth in Alvy Ray’s paper, but it does mean that the perfect reconstruction isn’t the same now that it was then.
Post reply on HN