I am amazed at the amount of birth stories with loads of graphic photographs you can find online..
I could never imagine putting such a personal and intimate thing in the public domain.
one i came across was the story of a baby girl born at 24 weeks who died soon after birth, and even had pictures of the funeral.
Personally I think its a special time for you and your partner. something you have created from love being born into the world. I would not have wanted to share this with anyone. Plus I hate my legs and wouldnt want anyone to see them!!
But of course this is only my own opinion and everyone will have different ones!!
In a way, the close ups might be better than the longer shots - less information to identify you in the street...
I personally think I would find it intrusive, but I know that a person who has filmed home births for documentaries is herself a midwife - so I don't know if that makes a difference to how unobtrusive she is with the camera.