Hi Matt,
 
That's tricky.  Copyright owners control the right to make derivatives of their work.  So, creating a new image using theirs could be construed as a derivative image, especially if you're using their entire image.
 
You could take a look at this Code of Best Practices in Fair Use for Media Literacy Education (http://www.centerforsocialmedia.org/fair-use/related-materials/codes/code-best-practices-fair-use-media-literacy-education) and see if it helps you with interpreting what you would like to do with the images.
 
Also, it doesn't matter if the image is common on the web.  What matters is who owns the actual image.  There are plenty of images on the web that are free to use or have creative commons licensing (but still require attribution) that may be better for you to start with.  This site (http://copyrightfriendly.wikispaces.com/) tries to link you to places with copyright friendly images.  
 
Laura
 
Laura Pope Robbins
Associate Professor/Reference Librarian
Dowling College / Library
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Oakdale, NY 11769
 
Phone: (631) 244-5023
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>>> Matt Amory <[log in to unmask]> 3/12/2012 10:51 AM >>>
I'm working with a set of images of artworks (images which are common on
the web for the most part) and I'm wondering if there is a way to layer
multiple "possibly-subject-to-copyright-claim" images together into a
single layered image which would not be subject to any copyright claim.

Since the GIMP'ed image I would be presenting would be different from any
of its constituent parts, could I post it without fear of takedown orders?
Or is this a dubious strategy?

Thanks for pondering

-- 
Matt Amory
(917) 771-4157
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http://www.linkedin.com/pub/matt-amory/8/515/239