Ask HN: Can data be owned by the individual creating it?

This is something I've been thinking about lately.

If you are walking across the street and I watch you do it, does that mean I need your permission to remember watching you cross the street (aka store data) and make decisions based on your previous actions?

Further, should I need your permission to tell other people about you crossing the street?

Seems to me that in this example, "data" (which is really just my interpretation of an observation) is owned by me and not you. It is after all my sensing & storage systems that collected the data.

What are your thoughts?