The first part of this book (Chapters 2–5) is devoted to a brief review of probability and probability distributions. Almost all models for computer vision can be interpreted in a probabilistic context, and in this book we will present all the material in this light. The probabilistic interpretation may initially seem confusing, but it has a great advantage: it provides a common notation that will be used throughout the book and will elucidate relationships between different models that would otherwise remain opaque.

So why is probability a suitable language to describe computer vision problems? In a camera, the three-dimensional world is projected onto the optical surface to form the image: a two-dimensional set of measurements. Our goal is to take these measurements and use them to establish the properties of the world that created them. However, there are two problems. First, the measurement process is noisy; what we observe is not the amount of light that fell on the sensor, but a noisy estimate of this quantity. We must describe the noise in these data, and for this we use probability. Second, the relationship between world and measurements is generally many to one: there may be many real-world configurations that are compatible with the same measurements. The chance that each of these possible worlds is present can also be described using probability.

The structure of Part I is as follows: in Chapter 2, we introduce the basic rules for manipulating probability distributions including the ideas of conditional and marginal probability and Bayes' rule.