I recently started reading the book Multiple View Geometry by Hartley and Zisserman. In the first chapter I came across the following concepts..
- Projective geometry is an extension of Euclidean geometry with two lines always meeting at a point.
- In Perspective geometry parallelism does not exist.
Then he goes on to explain how the points at infinity in the world like the points at the horizon appear as a line in the image of the world taken by a camera. Then he says a line which I cannot relate is the following..
The geometry of the projective plane and a distinguished line is known as Affine Geometry and any projective transformation that maps the distinguished line in one space to the distinguished line of the other space is known as an Affine transform.
I have the following questions...
- Is the camera plane the projective space of the real world?
- Is the line which is the image of the horizon the distinguished line?
- Whenever we do an Affine transform do we need to look out for a distinguished line?
- Why does just a distinction of the geometry a line in the perspective plane make the geometry an Affine geometry?