The Magic Kernel

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2024-10-06 11:00:05

This research paper (62 pages) provides a full mathematical description and analysis of the Magic Kernel and Magic Kernel Sharp:

There was some discussion of this paper when it was trending at #5 on Hacker News on March 22, 2021. There has also been some discussion on its Facebook Page. What is “the magic kernel”?

“The magic kernel” is, today, a colloquial name for Magic Kernel Sharp, a world-beating image resizing algorithm, superior to the popular Lanczos kernels, which has helped power the two largest social media photo sites in the world, Facebook and Instagram.

I originally came across what I dubbed at that time a “magic” kernel in 2006 in the source code for what is now the standard JPEG library. I found empirically that this “kernel”—in reality just interpolation weights of 1/4 and 3/4—allowed an image to be doubled in size, as many times as desired, astonishingly clearly. Experts pointed out, however, that the resulting images were slightly blurrier than an ideal resizer would produce.

In 2011 I investigated the remarkable properties of this “magic” kernel in depth, as a hobby, and generalized it to allow resizing an image to any arbitrary size—larger or smaller. I dubbed this generalization “the Magic Kernel.”