Digital Geometry in Image Processing

Distance Functions in Digital Geometry 37

Reprinted from Sadhana 18(1993), P. P. Das and B. N. Chatterji, Digital Distance Geometry: A Survey, 159–187,

Copyright (1993), with permission from Indian Academy of Sciences.

FIGURE 2.4: A minimal O(2) or 18-path between two points (2,-7,5) and

(-8,-4,13) in 3-D.

the algorithm, z ∈ Σ

n

∩N eb(y; N(·)), is chosen if Π

∗

(y, 0) is a concatenation

of Π

∗

(y, z) and Π

∗

(z, 0) (evidently, |Π

∗

(y, 0)| = |Π

∗

(y, z)| + |Π

∗

(z, 0)|). In

Algorithm 3 we illustrate such a choice for O(m)-neighborhood set for d

n

m

distance.

2.2.3 Distances and Metrics

In Z

n

, Euclidean distance E

n

is defined as follows:

Definition 2.11. In n-D, E

n

: Z

n

×