# 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.

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