Digital Geometry in Image Processing

List of Tables xxvii

Symbol Description

Sets and Spaces

R The set of all real numbers.

R

+

The set of positive real numbers.

Z The set of all integers.

N The set of all non-negative integers.

P The set of positive integers.

Q The set of rational numbers.

Z

N

{0, 1, 2, . . . , N − 1}

.

C The set of all complex numbers.

L

2

(R) The space of all square integrable

functions.

L

2

(Z) The space of all square integrable

functions over the integer grid.

[a, b] {x|x ∈ R and a ≤ x ≤ b}

(a, b] Left open, right closed interval, i.e.

{x|a < x and x ≤ b}.

u

(or u) u ( or u) is a point in Z

n

or R

n

and

also denoted as

u

= (u(1), u(2), . . . , u(n))

(or u

= (u

1

, u

2

, . . . , u

n

)).

|u

| Norm of