# Projection Matrix (Computer Vision)

I'm trying to understand a piece of code that is using a camera projection matrix. The camera projection matrix $P = \left[\begin{array}{c}p_1^T \\ p_2^T \\ p_3^T\end{array}\right]$ takes a point $X$ in 3D world coordinates and projects it onto pixel coordinates $x$ of an image. It is a $3 \times 4$ matrix. The 3rd row $p_3^T$ is the optical axis of the camera (neglecting the 4th element). The 1st and 2nd rows also correspond to the x and y axes if I normalize them.

In the piece of code I am working with, the norm $\|p_1^T\| + \|p_2^T\|$ is calculated. Any idea what this quantity could represent? It is called a "scale" factor.

• hey, have you looked around the site a bit? Check out this questions/answers,maybe they can help: 1, 2, 3 – penelope Dec 5 '12 at 9:10
• I have a clue that the projected points are in 2D homogenous coordinates $(x, y, w)$ where the $w$ "coordinate" is sometimes called weight. – Libor Dec 5 '12 at 14:17
• could you be a bit more clear about the 3rd row being the optical axis of the camera and the 1st and second corresponding to x and y? – Hammer Dec 5 '12 at 16:35
• Oh I just meant that if the third row $p_3^T = [p^1 p^2 p^3 p^4]$, then the optical axis of the camera can be obtained as optixal_axis = $\frac{p^1}{\sqrt{(p^1)^2 + (p^2)^2 + (p^3)^2}}, \frac{p^2}{\sqrt{(p^1)^2 + (p^2)^2 + (p^3)^2}}, \frac{p^3}{\sqrt{(p^1)^2 + (p^2)^2 + (p^3)^2}}$. – Mustafa Dec 5 '12 at 17:07
• Have you been able to find an answer? If you have, would you be able to post it? – Phonon Oct 27 '13 at 6:01