Homographies: Looking through a pinhole

I wrote this because I needed to calculate transformations between two cameras’ point of view and I just couldn’t find something accesible and straightforward. Hopefully somebody finds it useful.

I have the sad feeling that this article is reinventing what is already well described, in unambiguous and accepted terms. Here I see a reinvention of terms, meanings, notations, which will make it harder for those who will use it through third-party libraries or try to understand it more deeply. I tried to find anything available by a simple google search.... and couldn't find it.

Therefore, I will get what I had the good fortune to come across also outside the Internet:

[1] Lectures on 3D computer vision. Very rich, detailed, mathematically very accurate. The best one I ever saw on the topic

[2], [3] OpenCV documentation, including camera model and estimation of its position, mutual position of cameras

[4] Some good Standford lectures

[1] https://cmp.felk.cvut.cz/cmp/courses/TDV/2022W/lectures/tdv-...

[2] https://docs.opencv.org/4.x/d7/d53/tutorial_py_pose.html

[3] https://docs.opencv.org/4.x/d1/de0/tutorial_py_feature_homog...

[4] https://web.stanford.edu/class/cs231a/course_notes/01-camera...