Digital Geometry in Image Processing

94 Digital Geometry in Image Processing

It is also easy to observe that such a pre- image of D is periodic in a sense.

This we state in the following theorem.

Theorem 3.2. Let D = {d

1

, d

2

, ..., d

n

} be a DSLS and let l be a CSLS whose

digital image is D such that l contains at least two points of D. If d

i

and d

j

are successive such points, then d

i

and d

j

determine a period on D. That is,

if k = j − i, t hen dist(d

h

, l) = dist(d

h

+ k, l) for 1 ≤ h ≤ n − k [4]. 

The following theorem helps us to find a pre-image of D that pa sses

through at least two points of D.

Theorem 3.3. If l is a CSLS that is a pre-image of DSLS D and l contains

two points of D, then l is a segment of one of the nearest support of D. 

Thus, we can make the following statement.

Corollary ...