Programming Computer Vision with Python

Chapter 4. Camera Models and Augmented Reality

In this chapter, we will look at modeling cameras and how to effectively use such models. In the previous chapter, we covered image to image mappings and transforms. To handle mappings between 3D and images, the projection properties of the camera generating the image needs to be part of the mapping. Here we show how to determine camera properties and how to use image projections for applications like augmented reality. In the next chapter, we will use the camera model to look at applications with multiple views and mappings between them.

4.1 The Pin-Hole Camera Model

The pin-hole camera model (or sometimes projective camera model) is a widely used camera model in computer vision. It is simple and accurate enough for most applications. The name comes from the type of camera, like a camera obscura, that collects light through a small hole to the inside of a dark box or room. In the pin-hole camera model, light passes through a single point, the camera center, C, before it is projected onto an image plane. Figure 4-1 shows an illustration where the image plane is drawn in front of the camera center. The image plane in an actual camera would be upside down behind the camera center, but the model is the same.

The projection properties of a pin-hole camera can be derived from this illustration and the assumption that the image axis is aligned with the x and y axis of a 3D coordinate system. The optical axis of the camera then coincides with ...