According to the ImageMagick forum, it looks like ImageMagick used to require ffmpeg for reading video files, but as of late 2013 it will use either ffmpeg or libav/avconv, whichever is installed.
It looks like ImageMagick does not declare a dependency on ffmpeg. Do you have it installed? If not, try sudo port install ffmpeg
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I don't recall why ImageMagick doesn't declare a dependency on ffmpeg, but it might be because I would guess that most people use ImageMagick only to manipulate images; I didn't even know it could produce a video from a set of images. Adding a heavy dependency like ffmpeg would add overhead that most people probably wouldn't need. But maybe we should add a variant to the port for this.
#42299 might be related or the same issue.
If you would like MacPorts to offer libav/avconv, please re-open #50039 and discuss there.