Flickr shared their story about speeding up resizing of images to near real-time.
TL;DR:
* Switch to GraphicsMagick a mature fork of ImageMagick (started in 2002) that is more efficient, smaller code base, more secure, runs faster. (Also used by Etsy).
* Switch again, to Ymagine. Another 2X improvement over GraphicsMagick.
* Switch again, to a GPU-based tool. Another 4X improvement. This GPU tool doesn't appear to be open-sourced, however.
* Only reliably store thumbnails of 2048px (if the original is larger). Generate the rest on-the-fly (from the 2048 one), with HTTP caching only.