[HN Gopher] Lanczos Interpolation Explained (2022)
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Lanczos Interpolation Explained (2022)
Author : tobr
Score : 160 points
Date : 2025-10-05 07:49 UTC (6 days ago)
(HTM) web link (mazzo.li)
(TXT) w3m dump (mazzo.li)
| jeffreygoesto wrote:
| Kind of related: https://johncostella.com/magic/ and its
| discussion https://news.ycombinator.com/item?id=41756205
| magicalhippo wrote:
| That was a very nice and detailed description of the Laczos
| filter. It gave some new perspectives that were not covered by
| the sources I've read earlier.
| wartywhoa23 wrote:
| Not only a very nice explanation, but it's also presented in such
| an aesthetically pleasing way! The layout, the typography, the
| colors..
|
| The blog is a thing of beauty.
| trhway wrote:
| Difference with Gabors kernels (that are in our visual cortex and
| what the first level CNN kernels look to converge to) is the
| scaling factor 1/t instead of e^(-t)
| adzm wrote:
| I know bicubic is similar to lanczos with less ringing and less
| sharp but still felt like a glaring omission not comparing it
| with lanczos. That said, great article and great details, I
| learned a lot.
| magicalhippo wrote:
| Author does explain why it in a footnote:
|
| _Cubic interpolation is not included in the showcase since it
| is a family of filters rather than a single filter -- most
| cubic filters used in practice end up looking similar to
| Lanczos, although probably a bit less sharp but with less
| ringing._
| jgalt212 wrote:
| So just one method with common paramters and display those.
| jgalt212 wrote:
| I came to say just that. Why are there no pictures comparing
| the two? A competent high school student could write a method
| that beats linear and nearest.
| nasretdinov wrote:
| It's fascinating how the "ringing" around the edges looks so much
| like JPEG compression that it took me around 10 minutes to stop
| ignoring it and actually start looking at the images properly
| Sesse__ wrote:
| It's the exact same phenomenon. :-) The high frequencies are
| abruptly cut off in both cases.
| zozbot234 wrote:
| The claim that the best interpolation kernel for 2d images is
| just a product of two Lanczos kernels in the X and Y directions
| seems wrong to me. Rather, there is a proper 2D analog to the
| sinc function known as the jinc, or "Sombrero" function
| https://en.wikipedia.org/wiki/Sombrero_function . (This function
| is mathematically related to the "Airy" ringing patterns found in
| the optics of lenses.) Resampling with a jinc-based circular-
| window kernel should show a far lower intensity of ringing
| artifacts compared to the simple composition of two 1D Lanczos
| filters.
|
| On a different point, when approximating a "brickwall" frequency
| spectrum an 'equiripple' pattern is generally considered
| desirable, and this will lead to a different kernel than the
| Lanczos approach does.
| rostayob wrote:
| (I'm the author)
|
| I don't really claim that Lanczos interpolation as presented is
| the "best" 2D interpolation there is. It is definitely popular
| though, and I couldn't find a source explaining how it is
| derived, so I thought it'd be an interesting topic for a blog
| post.
| petermcneeley wrote:
| Thank you for this article. Are the graphs images? and how
| were they generated?
| hilbert42 wrote:
| An interesting article, especially given the links to the YouTube
| interview of Cornelius Lanczos. I've used the Lanczos algorithm
| for years for interpolation but until now I'd not put a face and
| voice to his work.
|
| It's interesting to compare Lanczos (and other) resampling
| algorithms in digital imaging with what's known as K-factor (aka
| K-rating)--a measurement in analog television for rating image
| quality. There are interesting similarities between the two.
|
| An image is an image whether it's generated digitally or by
| analog means, so it's only to be expected that ways of measuring
| image quality between these two systems would have some things in
| common. That's done by comparing the output signal with the
| original image but it's not as straightforward as it seems as
| human perception and subjectivity get in the way.
|
| As per article we've seen Lanczos, (sync, (sin x)/x) resampling
| quality is better than say nearest neighbour, Mitchell, triangle,
| etc. but the problem of human subjectivity remains as it's often
| difficult to compare image quality visually and or consistently.
| Analog television has long had methods of objectively evaluating
| images without the human factor and again the solution is
| mathematical, and as I'll show it has some interesting parallels
| with Lanczos resampling.
|
| To determine image quality/K-factor of a television transmission
| system an electronic test signal replaces the subjective image
| and it's measured for distortion products after it exits the
| system. The mathematical parameters of this test signal are
| carefully defined to detect distortions and artifacts that are
| most noticeable to the human eye.
|
| The test signal consists of a sine-squared pulse of specified
| duration followed by bar (a square wave with a transient response
| the same as the pulse). The K-factor is determined by measuring
| the deviation in the pulse and bar risetimes together with
| generated artifacts such as ringing and under and or overshoot.
| As the Pulse & Bar is a precision test signal input/output
| comparisons aren't necessary, thus a single measurement
| simplifies testing.
|
| For those interested see BBC Monograph 58 'Sine-squared Pulse and
| Bar Testing in Colour Television'. 1965. PDF
| https://www.bbc.co.uk/rd/publications/bbc_monograph_58
|
| Unfortunately, this ref. is behind a firewall: Macdiarmid, I.F.
| and Phillips, B. 'A Pulse & Bar Waveform Generator for Testing
| Television Links.' Proc I.E.E. Vol. 105, Part B, p.) 440. 1958.
| sfpotter wrote:
| One way to think of the sinc function is as the reproducing
| kernel (the point evaluation functional) for the space of
| bandlimited functions, thought of as a reproducing kernel Hilbert
| space. I guess the Shannon/Nyquist theorem just kind of falls out
| of this.
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