I remember trying to work this out. It turns out that the geometry parameter is just a string that describes the dimensions of either the finished image or the working area. eg:

my $ret = $image->Resize( geometry => "100x100" );
die "... $ret" if $ret;
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just tells IM to resize $image to 100 pixels square. The value can be more complicated, as in your Crop example where the offsets are also defined. I imagine the complex string parameters can be blamed on the command-line origins of all these tools.