Depends. Have you got a written employment contract that says that all the proceeds, results, etc. of your work belongs to your employer? If so, the employer owns the photos and their copyrights.
If not, you write that you were on a "field assignment," which means that you took these photos on the employer's time that they were paying you for. So even without an employment contract, I'd say they have a pretty good claim to the photos and to their copyright. Your claim isn't bad either, but if I were you, I wouldn't want to claim ownership of something I did on company time.
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On your employer's time, while working on assignment for your employer, you took photographs of your fellow employees. Though your employer did not ask you to take the photographs, and you weren't hired to do so, did a supervisor see you taking the pictures and permit you to take the time to continue photographing the company's employees and jobsite [tacitly tasking you to do so]? Did your fellow employees believe you were taking the pictures merely for your own personal benefit or did they think you were doing so for your employer?
As noted by Attorney Koslyn, your employer may have a very good argument that it owns the copyright in the photographs. But you could have an argument as well. Only your own copyright attorney can pass on the matter after all the facts are put on the table -- and after discussing why any of this matters.
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This could easily be argued reasonably and strongly for either side. Sounds like a law school homework assignment. My colleagues have given you the likely company arguments. You have given the arguments for the employee. The practical result is few companies would need, want, or ask for ownership and most would ask only for a license to use these photos for any company purpose, with right to sublicense. And few employees would object. In 20 years as in house counsel i handled such photo issues twelve times that i can recall and each time the employee was very eager to see their photos used and disappointed if someone else's were used instead. The only conflict over this i faced was when some employee was insisting that they were being discriminated against when their photos were NOT chosen for company use. And that is why i am betting this is a law school question - close legal question based on a highly improbable conflict where an easy and fast amicable settlement would almost always occur.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.