
Chapter 2
Distance Functions in Digital
Geometry
2.1 Mathematical Definitions and Notation . . . . . .. . . . . . . . . . . . . . . . . . . 29
2.1.1 Properties of Integer Functions .. . . . . . . . . . . . . .. . . . . . . . . .. 30
2.2 Neighborhoods, Paths, and Distances . . . . .. . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 Neighborhoods . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . 31
2.2.1.1 Characterizations of Neighborhood Sets . . . 31
2.2.2 Digital Paths . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . .. 34
2.2.2.1 Shortest Path Algorithm . . . . .. . . . . . . .