Creating a copyright on one's likeness seems pretty messy in regards to that, but there is a somewhat similar idea in German law (and surely other places) that creates similar concerns for using an image or work.

We have a "right to one's image", you generally can't distribute/publish photos with recognizable people without consent. Unless they're truly just "part of the landscape" (background randos), crowds at public events, or of legitimate news/artistic interest.

I'd expect a similar threshold to apply to this Danish solution.