Comment by raphlinus | Hacker News Reader

Comment by raphlinus | Hacker News Reader

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 lines (relevant to text), what gamma curve gives the perception of equal line thickness across the range of subpixel phase? How does it vary with display dpi? (Hint: it's likely not linear luminance)

* 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)

I've seen a number of discussions where people feel they are able to answer these questions from first principles, and corresponding arguments that doing these in a "correct" way gives results that are less visually appealing than the common assumptions of treating a pixel as a little square (so doing a box filter for reconstruction) and ignoring gamma so effectively using a perceptual color space for the purposes of alpha compositing.

I posit that these questions cannot be solved by argumentation. I think user studies might not be very difficult to do; you could probably get "good enough" results by doing online surveys, though this wouldn't pass standards of academic rigor.

> * 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 and white lines. By framing this as a question about gamma, you’ve implicitly assumed that “ideal” black lines on white would have equal perceived thickness to “ideal” white lines on black.

This is not the case, as typographers have known for decades. The right way to draw perceptually equal-thickness black-on-white and white-on-black lines is to vary the line width (perhaps even by more than a full pixel if the lines are thick enough!). Gamma only comes in afterwards, to help us reproduce the varied widths accurately, and the accurate way to do that is in a linear color space.

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.

As a simple demonstration, here's an image of a 1px white-on-black line and a 1px black-on-white line: https://imgur.com/a/9d9Tu3x

It's axis-aligned and box-filtered so there are no shades of gray, which means gamma is irrelevant. The white-on-black line appears to have a greater thickness than the black-on-white line.

There's a lot of empirical research showing that reading performance is better with positive-polarity (black-on-white) text than with negative-polarity text [1, 2], probably because the higher overall luminance results in a smaller pupil size and thus a sharper retinal image [3]. So, white-on-black lines appear thicker than black-on-white lines because the eye doesn't focus as sharply on them. This is true regardless of which color space blending is performed in.

Given this fact, if one wants to achieve uniform perceptual line thickness for black-on-white and white-on-black text, a more principled approach than messing with color blending would be to vary line width or the footprint of the antialiasing filter based on the luminance of the text (and possibly the background). This is the approach Apple and Adobe have taken for years with stem darkening/font dilation.

[1]: http://jdobr.es/pdf/Dobres-etal-2016-Displays.pdf

[2]: https://www.uni-duesseldorf.de/home/fileadmin/redaktion/Oeff...

[3]: http://www.psychologie.hhu.de/fileadmin/redaktion/Oeffentlic...

One caveat, if viewing this image on a high-dpi display there will be blurring from image upsampling by the browser. My eyes have the same result as yours: the white line appears thicker than the black one.

Here's the interesting thing about your observation: doing alpha compositing of text in a perceptual space (as opposed to a linear space) results in a thickening of black-on-white and a thinning of white-on-black. So doing gamma "wrong" actually results in better perceptual matching.

Do you have evidence that either Apple or Adobe varies the amount of stem darkening based on text luminance? I've tested Apple (macOS 10.12 most carefully) and have not seen this.

I don't think they actually take luminance into account (although I personally like the idea); I just meant that they solve the problem of "black-on-white text looks too thin" by thickening the text, rather than messing up other parts of the pipeline.

Absolutely, and I think there's a very strong case to be made for that. One of the points I'm trying to make is that you have to solve it somewhere. People who focus narrowly on "correct gamma" often miss this, especially when "incorrect gamma" is also plausibly a workable solution.

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 free, as opposed to doing a similar correction after something has been composited correctly.

Reeeaallly? I haven't made the images, but my intuition is telling me that text will be noticeably blurry compared with a box filter.

I basically agree with your points regarding compositing in a linear space, except that I suspect that thin black-on-white lines will come out looking thin and spindly.

It sounds like you are talking about text that doesn't move.

If you want a general filter that can give a result without visible aliasing while sacrificing as little sharpness as possible, a 2.2 gauss filter is very hard to beat and I have spent a lot of time trying.

Box filters can be sharper, lancoz filters can be better for scaling down a final image, etc. but they will alias in a general sense. You might not see it in static text which is fine.

Also thin black on white lines are an extreme outlier, since what you percieve is relative and the entire image matters. It is more into the realm of optical illusion that play off our relative sensitivity.

So obviously text is one of the things I care about a lot. I'm willing to accept your filter as being very good for a lot of stuff other than presenting a GUI.

Does this mean that there is not one true right answer for images, as there is for audio[0]? That you should use different reconstruction filters depending on the application. Is it accurate to say that a pixel is not a little square unless you're rendering text, in which case it is?

[0] I know this is a slight oversimplification, if you care deeply about latency you might choose between linear and minimal phase, etc. But for consumer applications it's true enough.

A Gaussian kernel will reduce ringing artifacts, but is much blurrier than alternative resampling kernels. https://www.imagemagick.org/Usage/filter/nicolas/

Does “diameter” here mean “twice the standard deviation”?

No, diameter means the width of the filter in pixels. Each side would extend 1.1 pixels for a 2.2 diameter filter.

If you compare filters at the same width, gauss will be softer, which is why you can lower the diameter.

A Gaussian filter has infinite support, and is characterized by its variance (or standard deviation). https://en.wikipedia.org/wiki/Gaussian_filter

A ‘Gaussian’ which extends 1.1 units is a non-standard and not clearly defined thing. Are you picking some fraction of 1.1 as the standard deviation and truncating after? (Often Gaussian filters are truncated after 3 standard deviations, or similar.) Are you multiplying by some other window function? ...

Can you link to a more explicit formal description of what you mean?

When I say 2.2 pixels as the diameter, I mean roughly that a pixel will be made up of all the samples 1.1 pixels or closer to the center of the pixel and they will be weighted by a gauss curve. How that gauss curve is actually used is not formal or strictly defined, but is usually a curve that goes out to about 3 standard deviation a baked into a LUT and normalized.

A curve that uses more standard deviations would have to be wider in pixels to look similar.

Do you have some code for what you specifically are talking about? Or a formal description?

You have been saying here “this kernel is better than all of the alternatives” but it’s hard to evaluate that kind of claim without knowing precisely what you mean.

“not formal or strictly defined” is not super encouraging.

I never said it was better than all alternatives, I said my experience is that it is difficult to beat in a general case.

Bake a gauss curve out to three standard deviations into a LUT and normalize it. You can look at what PBRT does.

Keep in mind that I was replying to someone confused by all the choice of filters and was giving him a very solid starting point. This isn't some grandiose claim of scientific exploration, it's experience.

Lanczos interpolation seems to beat a gauss filter for me. It has some overshooting/ringing effects of course, but the improved sharpness is a great tradeoff compared to the blurriness of gauss filtering. Of course, gauss filtering might still play a residual role in analog systems, such as the one that physically displays stuff via a CRT screen.

True, but how often do you care about the general case? Most images are representations of real objects, or symbols or diagrams designed for human comprehension. Ignoring cases that in practice are very unlikely to occur lets you optimize for the more common cases. Techniques like resizing in a sigmoidal color space (see http://www.imagemagick.org/Usage/resize/#resize_sigmoidal ) don't have any rigorous mathematical basis, but they're tuned subjectively to have good results in common cases.

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.

Were all the filters being compared with the same width? At the same width it will be softer, at a smaller pixel radius is where you can compare aliasing with the same visual sharpness as something like catmull-rom.

There were a variety of widths, it was one axis of the study. But I don’t remember the details, it is certainly possible you’re talking about something we didn’t test. Personally, at first I couldn’t even see the differences they were discussing.

Having studied graphics and signal processing for a few years in graduate school before that job, I thought I would be good at seeing the differences, and I was a bit shocked how good they were at it, and how not that good I was. :)

Truncating the Gaussian too closely though, and it’s not exactly a Gaussian anymore, you lose the best antialiasing properties. I can totally see how it will be sharper and more comparable to other popular filters. (Normalized & truncated at 1.1 radius is just slightly outside the 1 std dev line, right?)

Gaussian is my personal choice for large format prints of images with extreme aliasing problems.

My experience has likewise been that film DP’s have extremely impressive visual acuity, memory for color, etc. Talented artists often have developed whole sets of skills that the rest of us are unaware are even skills. In the same way a programmer might have thought about cache line false sharing as it affects memory hierarchy throughput, visual art often hides lots of expertise you cannot directly perceive, even as you can sense the quality of the whole.

I like to describe “learning to draw” as “installing a 3d modeling and rendering package on your brain, along with a decent collection of base models to modify”. It’s a complex skill set. If you start animating you get to add in a physics simulation. And you become conscious of so many little things that the layman only notices when you get it wrong.

If you want to see really careful observation skills, try dye-transfer printers like http://ctein.com/

The width of the filter is separate from how the gauss curve is used as a filter (and not everyone does it the same).

Using only one standard deviation cuts off a huge amount of the curve, ideally it would be cut off around the third standard deviation and normalized so that the value after the last would be zero.

> Having studied graphics and signal processing for a few years in graduate school before that job, I thought I would be good at seeing the differences, and I was a bit shocked how good they were at it, and how not that good I was. :)

IMO the best place to learn to see these distinctions is in careful photo printing (of the type where you spend >30m per image, and where “printing” here is being used in an old-school sense of “all of the manual steps to take a raw image from the camera and turn it into printed output”).

Spend a few months doing that for a few hours per week and your ability to see artifacts, textural details, fine differences in amount of edge contrast, etc. will shoot up. (Obviously the folks who spend 30 years on this are even better.)

Studying signal processing, optics, psychophysics, etc. is also useful for understanding what you are noticing, but it isn’t seeing practice.

There likely is tons of research on this in psychophysics (https://en.wikipedia.org/wiki/Psychophysics). I’m not familiar with it, but I do know that you’ll find that it isn’t as simple as what you state. For example, Google gave me http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.108.... I don’t know whether it’s good, or when it was written.

The perception of equal line thickness may depend on orientation of the lines (https://res.mdpi.com/vision/vision-03-00001/article_deploy/v...), distance from the fovea, distance from where your attention lies (a can of worms even deeper. I don’t think there’s agreement on whether one can attend to more than one visual location at a time, or what ‘attention’ even is), direction of those distances (vertical will almost certainly be different from horizontal, sight could be better or worse in the nasal direction vs the temporal one), light/dark adaptation of the eyes, whether subjects are color-blind, etc.

I fear that, to qet something that’s better than Weber’s law (https://en.wikipedia.org/wiki/Weber–Fechner_law), you need a model so complex that it doesn’t make sense to start using it.

It's possible this research has been done, but if so I haven't seen it yet. Basically the reason I feel confident asserting it is that I'm talking very specifically about the stimulus produced by modern displays. I know there's some work by Avi Naiman on CRT displays from the very early 90's[0]. There might be some other work done on low-resolution LCD's, but even aside from resolution it's only modern, high quality displays that have good contrast and low dependence on viewing angle (which affects gamma greatly).

Another place to look is Kevin Larson's work on subpixel rendering, which informed Microsoft's ClearType efforts. But that was done mostly around 10 years ago, when displays also were different. A good representative is [1].

Here's another pretty good paper I found[2], but it focuses more on the display technology than the perception side.

So what I'm looking for is adjacent to general psychophysics results on visual perception, but much more specific to what real displays do. That literature is pretty thin on the ground.

[0]: Avi C. Naiman and Walter Makous. Spatial nonlinearities of gray-scale CRT pixels, 1992

[1]: https://www.researchgate.net/publication/264485766_Optimizin...

[2]: https://pdfs.semanticscholar.org/8fc4/ecc59380f24e363c6a5d6a...

There is research about perception of physically printed lines, done by e.g. print photography companies decades ago.

There is plenty of formal signal processing analysis of the aliasing artifacts at different angles created by grids of pixels.

The ImageMagick folks did a bunch of experimentation about resampling filters as used in arbitrary transformations of existing raster images. https://www.imagemagick.org/Usage/filter/nicolas/ – of course what looks best depends significantly on (subjective) preferences and on what the source image is.

So based on this research, what reconstruction filter and gamma curve should I use to render text so it looks good over a range of fonts? :)

Or, perhaps a better posed question. What research-informed model will accurately predict the results of a user study that presents various renderings of antialiased lines on a modern LCD monitor and asks subjects to choose "which line is thicker" types of queries?

Also does the font have variable weight? Are you adjusting it in any other way before rendering? What context were the fonts designed for – did the font designers evaluate their appearance using any specific displays / rendering engines?

> asks subjects to choose "which line is thicker" types of queries

I think you could develop a model for “which line is thicker” given a specific target display without inordinately much trouble; you might have to tweak some parameters for matching particular displays. The harder question is “which line is the right thickness”, especially if you don’t have any correct answers to reference.

We also don’t just care about apparent line thickness but also spatial resolution, aliasing artifacts, ...

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