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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 4connected because q / ∈ N 4 ( p ) b) S 1 and S 2 are 8connected because q ∈ N 8 ( p ) c) S 1 and S 2 are mconnected because q ∈ N D ( p )& N 4 ( p ) ∩ N 4 ( q ) = ∅ Figure 1: Q2 . We wish to transform an 8connected one pixel thick path to a 4connected 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 . 4connected : As shown in Figure 3a, there is no 4path between p and q since one cannot reach q from p by traveling along points that are 4connected and have values in V. 8connected : As shown in Figure 3b, the shortest 8path has length 4 and is unique. mconnected : As shown in Figure 3c, the shortest mpath has length 5 and is unique. b) 4connected : As shown in Figure 3d, q can be reached from p along the shortest path of length. Note that this path is nonunique as the dashed line shows another path of the same length. 8connected : As shown in Figure 3e, the shortest 8path has length 4 and is nonunique. Check the dashed line for an alternative. mconnected : The shortest mpath is nonunique and has length 6. The paths coincide with the shortest 4paths....
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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
 MANJUNATH

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