I've cropped this below picture from the journal: A Robust Visual Odometry and Precipice Detection System Using Consumer-grade Monocular Vision
Here it says,
- $(u,v)$ denotes for pixel coordinate and $(x,y)$ denote the coordinate of 2D ground plane. $u$ increment from left to right and $v$ increment from top to bottom of the frame.
- $U$, $V$ are the width and the height of image in pixels respectively.
- VFOV & UFOV are field of view angles in vertical direction and, horizontal direction respectively.
- $H$ is the height of the camera center from the ground and $D$ is the distance between the robot to the intersection of the principal ray.
What I didn't understand is, that the above journal states these following trigonometric relation:
$$\tan\beta = (2v-V)\tan(\text{VFOV}/2)$$
$$ z = {H \cos\beta\over\sin(\alpha + \beta)}$$
I would much appreciate if someone can help me out on this. Please check the page 3 of the paper if need more clarification on this.
Thanking You!