The axes planes:

Consider points on the plane ${\bf\pi}_1^T$ . This set satisfies

$${\bf\pi}_1^T{\bf X} = 0$$

and, hence, points on this plane project on to image points $(0,y,w)$ , which are points on the image $y$ -axis. It also follows from $\tilde{\bf P}{\bf C} = 0$ that ${\bf C}$ also lies on ${\bf\pi}_1^T$ . Hence ${\bf\pi}_1^T$ is the plane defined by the optical center and the $y$ -axis in the image plane.

Similarly, ${\bf\pi}_2^T$ is the plane defined by the optical center and the $x$ -axis in the image plane.

Thus unlike ${\bf\pi}_3^T$ , ${\bf\pi}_1^T$ and ${\bf\pi}_2^T$ are dependent on the choice of the coordinate system on the image plane. In particular, the intersection of these two planes is the line joining the optical center with the coordinate origin in the image plane. This line will not, in general, coincide with the principal axis defined below.