Projection Models

Overview

Here we introduce the two major projection models used by PyTorch3D:

• The perspective projection

• The orthographic projection

The projection models

Projection models essentially describe yet another coordinate space transformation. They provide a complete picture of how we transform 3D world space objects into 2D image space renders. They dictate mathematically how light passes through the 3D world onto the image plane. We’ll talk primarily about perspective projection and orthographic projection.

The difference between perspective projection and orthographic projection essentially comes down to differences in the orientation of light rays that make up the image plane. In the perspective model, all rays of light that enter a camera cross over at the same point in 3D space, the optical center (recall that, in reality, they actually pass through a disk-shaped aperture rather than a single point). That means that the vector that passes through each pixel in the image plane is slightly different from the others.

The vanishing point technique

The vanishing point technique comes up quite frequently in art courses. We know that the lines of the hallways and buildings in a classic painting are parallel in reality, and yet they all seem to converge to the same point along the horizon. This is precisely because this technique mimics the effects of perspective projection. The effects of projection mean that distant points shrink toward the optical axis, and closer points expand away from it.

Contrast this to an architecture diagram, for instance. There are no effects of perspective projection—and therefore of depth—visible in an orthographic projection. The windows that are far from the viewer are the exact same size as those that are close. In an orthographic projection, everything along a given dimension is represented at its relative size to one another.

The perspective projection

When we were speaking before about the pinhole camera model and camera frustums, we were referring specifically to perspective projection. This is the mode of projection most often encountered in the real world, where distant objects appear small and nearby objects appear large.