Effectively you are asking, when is a derivative work legal?
Two important tests to be applied are
1) Originality
The derivative work "must display some originality of its own. It cannot be a rote, uncreative variation on the earlier, underlying work. The latter work must contain sufficient new expression, over and above that embodied in the earlier work for the latter work to satisfy copyright law’s requirement of originality."
2) Transformativeness
"Transformativeness is a concept used in United States copyright law to describe a characteristic of some derivative works that makes them transcend or place in a new light the underlying works on which they are based."
"The use must be productive and must employ the quoted matter in a different manner or for a different purpose from the original. ...[If] the secondary use adds value to the original--if the quoted matter is used as raw material, transformed in the creation of new information, new aesthetics, new insights and understandings--this is the very type of activity that the fair use doctrine intends to protect for the enrichment of society."
Using your example, where a photo is simply reproduced in another medium, such as oils, it fails both tests:
- Originality, it is a rote, uncreative variation of the original work.
- Transformative, it does not add new information, new aesthetics, or new insights and understandings.
All quotes taken from Wikipedia.
For a further discussion see this very interesting article by Professor Stern
L.H.O.O.Q.--Internet-Related Derivative Works