Generalized Camera Models

Standard cameras are central—all rays pass through a single optical center. However, multi-camera rigs (like those on self-driving cars) are non-central. Rays from different cameras do not share a common convergence point.

Plücker Coordinates

In a Generalized Camera Model (GCM), we represent each light ray as a Plücker line $\mathbf{L} = (\mathbf{u}, \mathbf{q})$.

$\mathbf{u} = \text{Ray Direction}$
$\mathbf{q} = \mathbf{c} \times \mathbf{u} \text{ (Moment)}$

Where $\mathbf{c}$ is the origin of the specific camera in the rig coordinate system.

The Non-Central Challenge

Because there is no single center of projection, a simple $3 \times 3$ homography cannot relate two views of a scene if the rig moves. The transformation depends on depth, creating a parallax effect that traditional central models cannot resolve.

Why Plücker? Plücker coordinates allow us to treat rays as basic geometric entities, enabling the 16-point and 17-point solvers used for robust motion estimation in multi-camera systems.
Car Body
Cameras
Rays ($\mathbf{u}, \mathbf{q}$)
Rig Rotation

Drag the car to observe how rays from 4 separate cameras move in the rig coordinate system.