The Lion King being remade in 3d

[etoven]

How does it tell what depth level it needs for each individual pixel? How does it know that Simba's nose should be sticking out and not caved in?

The filter isn't perfect, but what it does is assume the image is drawn using proper perspective and renders the image based on calculated depth based on that perspective, assuming the footage is shot in a decent manner it works pretty well. It's a very complicated algorithm that tracks the position of a pixel in 3D space from a 2D plane. It's kinda the reverse of what a 3D engine does (projecting a 3D point on a 2D space). It's basically the same math in reverse. If your curious, a good program that does it is here, the page also has some good resources on the process.