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Unformatted text preview: HW #2 Solutions Anindya Sarkar & Emre Sargin Q1 . p and q are connected according to Figure 1 a) S 1 and S 2 are not 4-connected because q / ∈ N 4 ( p ) b) S 1 and S 2 are 8-connected because q ∈ N 8 ( p ) c) S 1 and S 2 are m-connected because q ∈ N D ( p )& N 4 ( p ) ∩ N 4 ( q ) = ∅ Figure 1: Q2 . We wish to transform an 8-connected one pixel thick path to a 4-connected path. Since N 8 ( p ) = N D ( p ) ∪ N 4( p ), we wish to define the changes that need to be done to those diagonal segments. The solution is merely by replacing any one of the diagonal segments in the boundary by the appropriate neighborhood from Figure 2. Q3 . 4-connected : As shown in Figure 3-a, there is no 4-path between p and q since one cannot reach q from p by traveling along points that are 4-connected and have values in V. 8-connected : As shown in Figure 3-b, the shortest 8-path has length 4 and is unique. m-connected : As shown in Figure 3-c, the shortest m-path has length 5 and is unique. b) 4-connected : As shown in Figure 3-d, q can be reached from p along the shortest path of length. Note that this path is non-unique as the dashed line shows another path of the same length. 8-connected : As shown in Figure 3-e, the shortest 8-path has length 4 and is non-unique. Check the dashed line for an alternative. m-connected : The shortest m-path is non-unique and has length 6. The paths coincide with the shortest 4-paths....
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This note was uploaded on 06/12/2009 for the course ECE 178 taught by Professor Manjunath during the Winter '08 term at UCSB.
- Winter '08