Goal of this article: Understanding how a point is mapped to a pixel coordinate and vice versa.

3D point is mapped into 2D plane.

Visualization for each coordinate systems

Relation between each coordinate systems

How extrinsic and intrinsic parameters are involved

• Extrinsic Parameters : Where are we in the process? : Describe the pose, therefore 6 parameters are necessary.

Convert the coordinate system from world'view to sensor view.

• Intrinsic Parameters : Process of projecting points from the camera coordinate system to sensor coordinate system.

1. Perspective projection to the image plane

If the camera is ideal, it is linearly projected.

The projection can be written in this matrix form.

It leads us to mapping.

H comes from extrinsic calibration. Now, conversion from o(origin) to c(image plane) is derived.

Matrices are written in this way. P maps a point to the image plane.

It yields for the coordinates of the image coordinates.

This leads to the collinearity equation for the image coordinates.