This chapter introduces the pinhole or projective camera. This is a purely geometric model that describes the process whereby points in the world are projected into the image. Clearly, the position in the image depends on the position in the world, and the pinhole camera model captures this relationship.

To motivate this model, we will consider the problem of sparse stereo reconstruction (Figure 14.1). We are given two images of a rigid object taken from different positions. Let us assume that we can identify corresponding 2D features between the two images – points that are projected versions of the same position in the 3D world. The goal now is to establish this 3D position using the observed 2D feature points. The resulting 3D information could be used by a robot to help it navigate through the scene, or to facilitate object recognition.

The pinhole camera

In real life, a pinhole camera consists of a chamber with a small hole (the pinhole) in the front (Figure 14.2). Rays from an object in the world pass through this hole to form an inverted image on the back face of the box, or image plane. Our goal is to build a mathematical model of this process.

It is slightly inconvenient that the image from the pinhole camera is upside-down. Hence, we instead consider the virtual image that would result from placing the image plane in front of the pinhole.