The page mostly talks about image resampling where the goal is more or less preserving all frequencies, but it's also extremely effective at implementing Gaussian blur. Basically, you do n iterations of sampling by 1/2 using this kernel, followed by a very small FIR filter, then n iterations of upsampling 2x using the same kernel. Here, n is essentially log2 of the blur radius, and the total amount of computation is essentially invariant to that radius. All these computations are efficient on GPU - in particular, the upsampling can be done using vanilla bilinear texture sampling (which is very cheap), just being slightly clever about the fractional coordinates.

It works well because, as stated, the kernel does a good job rejecting frequencies prone to aliasing. So, in particular, you don't get any real quality loss from doing 2x scale changes as opposed to bigger steps (and thus considerably larger FIR support).

I feel like this article is really overselling this filter. A 4-point symmetric interpolation kernel can be parameterized as [k, 1-k, 1-k, k]/2, i.e. it has a single degree of freedom. k=-1/4 is bicubic, k=1/4 is this 'magic', and k=0 is bilinear. Bicubic is sharper, and 'magic' has better alias rejection. Which looks better depends on the image and the viewer's subjective preference. For insta photos, it's probably better to go for 'magic', while for text, one might prefer bicubic. Neither is "simpler" as this article keeps suggesting, they just have different filter coefficients, that's all. But any other value of k is an equally valid choice.

> Fourthly, and most importantly, as noted above: m(x) is a partition of unity: it “fits into itself”; [...] if we place a copy of m(x) at integral positions, and sum up the results, we get a constant (unity) across all x. [...] This remarkable property can help prevent “beat” artifacts across a resized image.

So, basically the reason why this works better than other visually similar filters is that it happens to satify the Nyquist ISI criterion[1].

[1]: https://en.wikipedia.org/wiki/Nyquist_ISI_criterion

This uniform b-spline is the same one used often as a "Gaussian" approximation (three box filters) - see Paul Heckbert's 1986 paper here (apparently done at NYIT in the early 1980s with help from Ken Perlin):

https://dl.acm.org/doi/pdf/10.1145/15886.15921

In the “Bicubic: note the artifacts” comparison images, the bicubic version, regardless of the aliasing, is less blurry and has more detail than the “magic kernel” version. I therefore don’t agree that the latter is “visually, far superior”. There is at least some trade-off.

I was surprised I hadn't heard of this, or his related project JPEG-Clear. I have thought for years that the JPEG-Clear method is how responsive images should have been handled in a browser. A single-file format that can be progressively downloaded only up to the resolution it is being displayed at. If you zoom in, the rest of the data can be downloaded for more detail. Doesn't require complex multi-file image authoring steps, keeps simple <img src> grammar, and is more efficient than downloading multiple completely separate images.

Would be cooler if images on FB didn't suck.

Super cool. How did I not know about this before?

These previous discussions (including the author in the second one) were pretty fruitful:

https://news.ycombinator.com/item?id=10404517 (2015)

https://news.ycombinator.com/item?id=26513518 (2021)

I guess anything is magic if you don't know how it works or if you need some clicks to promote your personal site.

This is basically a slightly different gaussian kernel and the "incredible results" of a small image becoming a larger resolution blurry image is completely normal.

Also you don't want negative lobes in image kernels no matter how theoretically ideal it is, because it will give you ringing artifacts.

If you work with image kernels / reconstruction filters long enough you will eventually learn that 90% of the time you want a gauss kernel.