Description:
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Gmagick::writeimage documentation 
(http://php.net/manual/en/gmagick.writeimage.php) says filename is optional. It 
should work without a filename if Gmagick::setimagefilename has been called.

it actually throws an exception if the filename is set to null. Calling the method 
withtout argument triggers a warning (Gmagick::writeimage() expects at least 1 
parameter, 0 given)

Imagick provides the same thing, see 
http://fr2.php.net/manual/en/imagick.writeimage.php

Test script:
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$gmagick = new Gmagick('duck.jpg');
$gmagick->writeimage();

or 

$gmagick = new Gmagick('duck.jpg');
$gmagick->writeimage(null);