Image Points and image lines – two viewpoints
In a previous post, I talked about the image points and image lines. In this post, I will talk about how to interpret the image geometry which is different from the geometry we learned before.
- Point of view I: good, easy
Let an image point with coordinates . A line passing the point is
Hence we denote as an image point and as an image line. Then we know:
a) a point is on a line iff
b) the line passing two points is
c) the intersection point of two lines is
Remark: This point of view is quite easy. No need to care what happens outside the image plane.
- Point of view II: a 3D interseption
Image point: The formula of the normalized image plane is . So the 3D coordinates of a point on the image plane is .
Image Line: A line in the image plane can be treated as the intersection line between a plane passing through the origin and plane . Note any plane passing through the origin is uniquely determined by its norm vector . Hence any vector
intersect with plane an image line
Any points on the image line must have since is orthogonal to all vectors in the plane
Remark: here we interpret them in 3D camera reference frame.