Perspective Projection Formula Reference
Hello, I'm learning some formula in relation to computer vision and came across this. How was the formula for x, y, and z formed?
Here's the referenced video (4:25 for time stamp): https://www.youtube.com/watch?v=hUVyDabn1Mg
Perspective Projection Formula:
$$(u^{}_{l},v^{}_{l}) = (f^{}_{x}\frac{x}{z} + o^{}_{x},f^{}_{y}\frac{y}{z} + o^{}_{y} ) $$
$$ (u^{}_{r},v^{}_{r}) = (f^{}_{x}\frac{x - b}{z} + o^{}_{x},f^{}_{y}\frac{y}{z} + o^{}_{y} ) $$
Formula for x, y, and z are as follows (from video):
$$ x = \frac{b(u^{}_{l} - o^{}_{x})}{(u^{}_{l} - u^{}_{r})} $$
$$ y = \frac{bf^{}_{x}(v^{}_{l} - o^{}_{y})} {f^{}_{y}(u^{}_{l} - u^{}_{r})} $$
$$ z = \frac{bf^{}_{x}} {(u^{}_{l} - u^{}_{r})} $$