Metrics
This chapter discusses metric spaces [S, d], in which S is a subset of Rn 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.
3.1 Basics About Metrics
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.
3.1.1 The Euclidean metric
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 ...
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