03-3D space rigid body motion-01-homogeneous coordinates and general coordinates

Not only in SLAM, there are many conventional assumptions in computer vision, which will bring certain difficulties to readers.

 

Take the conversion from world coordinates to pixel coordinates as an example:

(For what are world coordinates, pixel coordinates, and image coordinates, you can refer to my video: https://www.bilibili.com/video/av22842726)

 

General coordinates:

P' represents the transformed point coordinates;

P represents the original point coordinates;
R is the 3X3 rotation vector;

t is the 3X1 translation matrix

Here P' and P are three-dimensional coordinates.

Homogeneous coordinates:

T is a 4X4 external parameter matrix;

Therefore, the corresponding P' and P should be four-dimensional vectors before they can be calculated. It is to add a 1 to the three-dimensional basis.

 

 It is a convention that when expressing RP and TP, depending on the situation, P is automatically selected as a form that satisfies the operation.