The relationship between Photogrammetry and computer vision coordinate system transformation and some basic quantities

This blog attempts to use some of the most intuitive, image, examples of the way to explain the relevant concepts

For learners of a photogrammetry (photogrammetry) or three-dimensional computer vision (3D computer vision), the first thing to contact is the conversion between various coordinate systems, and the Photogrammetry field has its own set of coordinate system rules, Computer Vision also has its own rules. Let's look at how they are transformed. Rotational Euler angles in photogrammetry are composed of rotation matrices R R (rotation), Baseline (baseline) b b and Computer vision in the rotation matrix (camera rotation) r R, translation vector (camera translation) T T, camera bit What is the relationship between (camera position) C C.

To answer these questions, we first give two very intuitive examples to clarify the rotation problem in three-dimensional space.
When it comes to the rotation in space, we need to pay special attention to two questions:
(1) The direction of rotation, that is, from a A to b b or from b b to a A;
(2) The rotation is clockwise (clockwise) or counterclockwise (counter-clockwise).
Of course, they are relative, clockwise from a A to B b is counter-clockwise from b b to a A. Well, that's so abstract, look at an example of a simple two-dimensional coordinate system:

Assuming that the coordinates of P p point in the o−xy O-xy coordinate system are (), what is the coordinate of P p point in the o1−xy o_1-xy coordinate system? From the figure we can see directly (1,−1) (1,-1). But how is it calculated in theory? We know that the coordinates of P p point under O1−xy O_1-xy are the o−xy o-xy coordinate system counterclockwise rotation π2 \frac{\pi}{2}, it should be noted that in the rotation of the coordinate system, p p Point does not change, we want to get only P P point in different sitting The representation of a standard system, then how to use a matrix to represent the process.
Here, we first directly give the two-dimensional coordinate system clockwise rotation Θ\theta formula (here do not deduce, interested can be deduced, but also very simple).
[cosθ