Nearest neighbor (simple)
A pixel becomes a square 2×2 block of the same color, then a 4×4, ...
Main advantage of this system: no calculation is necessary, so it is blazing fast. This is actually the way your browser upsizes images.
This is slightly better than the naive method. For mathematical details, check the Hermite Interpolating Polynomial.
Bilinear interpolation considers the closest 2×2 neighborhood of known pixel values surrounding the unknown pixel. It then takes a weighted average of these 4 pixels to arrive at its final interpolated value. This results in much smoother looking images than nearest neighbor.
Acceptable quality. Images are sometimes too smooth.
Lanczos is the most complex, and slowest method, which should give the best results.
So here's a roundup of some interpolation algorithms for making images bigger. Keep in mind that larger resolutions cause larger files. An image good enough for A0 printing (14000 x 10000 pixels) could amount to a 800MB TIFF file. Don't send them through email.
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