Digital Image Processing

1. Lecture 4: Pixel Relationships Examples
©2017Eng.Marwa_M_Ahmeid Page 1
1-Consider the image segment shown below.
(a) Let V = {0, 1} and compute D4-, D8- ja Dm-distances between p and q.
(b) Repeat for V = {1, 2}.
a) D4(p, q) = |xp - xq| + |yp - yq| = 3 + 3 = 6
D8(p, q) = max(|xp - xq|, |yp - yq|) = max(3, 3) = 3
Dm(p, q) = 5
b) D4 and D8 are independent of V, so they are the same as in a).
Dm(p, q) = 6
Of course, this is not the only possible path with length 6.

2. Lecture 4: Pixel Relationships Examples
©2017Eng.Marwa_M_Ahmeid Page 2
2-Consider the two image subsets S1 and S2 shown below. For V = {1}, determine how
many
(a) 4-connected
(b) 8-connected
(c) m-connected
components there are in S1 and S2. Are S1 and S2 adjacent?
Connectivity: “Are there certain pixels in the neigbourhood?”
Adjacency: “Are certain pixels adjacent?”
a) 4-connected components:
S1: 1, S2: 3
b) 8-connected components:
S1: 1, S2: 1
c) M-connected components:
S1: 1, S2: 1

3. Lecture 4: Pixel Relationships Examples
©2017Eng.Marwa_M_Ahmeid Page 3
The answer is the same as in b), but now there exist only one possible path connecting the pixels.
Adjacency:
a): S1 and S2 are not adjacent, since no pixel of S2 that belong to V is a 4-neighour of any
pixel in S1 that belong to V .
b) and c): In both the cases S1 and S2 are adjacent, thanks to the pixels that have been circled
in the figures.
3.1-Consider the image segment shown.
(a)Let v={0,1} and compute the lengths of the shortest 4-, 8-, and m-path
between p and q. If a particular path does not exist between these two
points, explain why.
(b) Repeat for V = {1,2}
(a) When V = {0,1}, 4-path does not exist between p and q because it is impossible
to get from p to q by traveling along points that are both 4-adjacent and
also have values from V . Figure P2.15(a) shows this condition; it is not possible
to get to q. The shortest 8-path is shown in Fig. P2.15(b); its length is 4. The
length of the shortest m- path (shown dashed) is 5. Both of these shortest paths
are unique in this case.
3.2-Consider the two image subsets S1 and S2 and shown in the following figure. For V={1}
determine whether these two subsets are (a) 4-adjacent, (b) 8-adjacent,
or (c) m-adjacent.
Let p and q be as shown in Fig. P2.11. Then, (a) S1 and S2 are not 4-connected
because q is not in the set N4(p); (b) S1 and S2 are 8-connected because q is in
the set N8(p); (c) S1 and S2 are m-connected because (i) q is in ND(p), and (ii)
the set N4(p) ∩ N4(q) is empty.

4. Lecture 4: Pixel Relationships Examples
©2017Eng.Marwa_M_Ahmeid Page 4
4- (a)Give the condition(s) under which the D4 distance between two points p
and q is equal to the shortest 4-path between these points.
(b) Is this path unique?

5. Lecture 4: Pixel Relationships Examples
©2017Eng.Marwa_M_Ahmeid Page 5
5-