Isn't the magic kernel simply a 2× bilinear downscale filter? For example, if you use 2× bilinear downscaling in Tensorflow (as opposed to bilinear downsampling which would end up being just a box filter) using tf.image.resize it uses the magic kernel [1,3,3,1].
There is an article [0] that points this out, although later it goes into recommending odd filters, which insidiously break many applications where you would want to use downscaling by shifting the image by a fraction of a pixel.
I discuss Charles Bloom's 2011 article in some detail on my page. The original "magic" kernel (i.e. [1,3,3,1]) can be rightly categorized as just many things. It's the generalization to the continuum case, and the addition of the Sharp step — and, now, to arbitrary higher "generation" 'a' — that makes it useful and more powerful. Bloom's post ten years ago inspired me to play some more with the "original" and figure out at least the "continuum" version.
There is an article [0] that points this out, although later it goes into recommending odd filters, which insidiously break many applications where you would want to use downscaling by shifting the image by a fraction of a pixel.
[0] https://cbloomrants.blogspot.com/2011/03/03-24-11-image-filt...