shared libraries for image loading

I'm looking for the library that handles image loading, particularly for .webp files. My motivation is to get emacs to display these images. My installation (18.04) is able to display these images when I'm in a web browser, so the functionality is there somewhere.

When I load a .webp file in emacs, it isn't recognized as an image file, and displays as garbage (well, the uninterpreted binary contents of the file). I have seen advice on this that includes making sure the correct image-loading shared libraries are in a place emacs knows to look for them. That's why I'd like to know the name of that file, and/or how to be sure the version of the file I have actually includes .webp support.