It comes down to the fact that imagemagick is built with support for the
X picture formats for flexibility. This requires the some X libs. Not
the WHOLE X binary setup, just some libraries. About 800K is all, vs
~100MB for minimal X.
To quote the file "/usr/share/doc/imagemagick/README.Debian"
5) We will not provide non-X11 binary package, because xlibs
package does not so big. If you really need non-X11 binary
package, you can build it without xlibs.
There in you get your answer.
And X11-common is a just that, to provide the needed locations and
skeleton files for the xlibs and a few minor libraries to function for
things like gd and imagemagick when built with xlibs support.