Are tattoos copyrightable?

Suppose I have a very fancy and intricate tattoo somewhere on my body. (I don’t, but just suppose) I designed it and the tattoo artists drew it on my body and it is excellent work.

Then suppose someone saw it, and maybe took a picture of it. (For the sake of this question, let’s say it was on my chest and someone snapped a picture of it at the pool.)

Next thing I know, they have the exact same tattoo on their body, every last detail.

Is that copyright infringement? Is my unique design covered by copyright? Can I sue for infringement?