Camera Parameters (Intrinsic and Extrinsic)

Overview

The projection matrix defines how we relate objects in the 3D world coordinate space to the 2D camera space. This matrix is composed of the extrinsic and intrinsic parameters of a given camera.

The extrinsic parameters

The extrinsic parameters describe the external properties of the camera, namely the camera translation and rotation. To briefly recap, translation is the three parameters describing the $(x, y, z)$ position of the camera. Likewise, rotation is the three parameters describing the rotations about the $x$, $y$, and $z$ axes. While rotation in 3D can come in many forms, this particular form of rotation is called the Euler angles of the rotation. Although intuitive, Euler angles are not the ideal form for actually applying rotations. For now, the PyTorch3D API makes it easy to specify rotations in Euler angles while handling the hairy details.

We most often use camera parameters in matrix form. The rotation is expressed as a $3\times3$ matrix $R$ and the translation as a $3\times1$ vector $t$. Oftentimes the rotation $R$ and translation $t$ are concatenated to create a single $3\times4$ matrix that we call the transformation matrix $T$.