CHAPTER 3

This chapter discusses metric spaces [*S, d*], in which *S* is a subset of R^{n} or a subset of a grid; it also addresses metric spaces, in which *S* is a family of such subsets. It also discusses metrics on pictures in which distances depend on the pixel values.

Measurement requires a metric space. In this section, we summarize facts about metric spaces that are relevant to digital geometry. The definition of a metric (distance function) based on properties **M1** through **M3** was given in Section 1.2.1.

We first consider the metric that is used in Euclidean geometry: the *distance* between two points is equal to the length of the straight line segment defined by the two points. This metric ...

Start Free Trial

No credit card required