Protection for Your Derivative Works
As the owner of a copyright, you have complete and exclusive control to do a variety of things to your photograph, including the right to prepare derivative works based on the original image. But when you alter a work, it's a judgment call as to whether it constitutes a derivative work or is only a minor variation of the original work.
A derivative work is one that is based on one or more earlier works. Derivative works include editorial revisions, annotations or other modifications. A derivative work must be different enough from the original to be regarded a new work - in other words, it must contain some substantial, not merely trivial, originality. Making minor changes or additions of little substance to a preexisting work will not make it a new version for copyright purposes.
One of the tests to decide whether the new work is a derivative work is whether the new material is original and copyrightable in itself. Note that, for reasons not covered here, the standard of originality is higher for derivative works than it is for those not based on preexisting works.
If your photo meets the definition of a derivative work, it must be registered for full statutory protection. If the photo only is slightly modified and does not qualify as a derivative work, then the original registration covers the work.
In the case cited above, since the photograph of the wheels may be considered original and copyrightable itself, adding it to the original photograph probably makes it a new work. For the most protection, registering the new work is the safest bet.
Take my advice; get professional help.
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