Pixel Relationships Examples
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The document discusses pixel relationships and connectivity in images. It contains examples calculating 4-connected, 8-connected, and maximally connected (m-connected) distances between pixels p and q for different value sets V. It also determines the number of connected components and adjacency between image subsets for different connectivity types. Key points made include: - D4, D8, and Dm distances were calculated between pixels p and q for value sets V={0,1} and V={1,2}. - The number of 4, 8, and m-connected components in image subsets S1 and S2 were determined, and whether the subsets were adjacent was discussed. - Shortest path lengths between p
Pixel Relationships Examples
- 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-