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Relationship between adjacent pixels in an image
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- 4. Relationship between pixels •Adjacency • Two pixels are connected if they are neighbors and their gray levels satisfy some specified criterion of similarity. • For example, in a binary image two pixels are connected if they are 4-neighbors and have same value (0/1) • Let v: a set of intensity values used to define adjacency and connectivity. • In a binary Image v={1}, if we are referring to adjacency of pixels with value 1. • In a Gray scale image, the idea is the same, but v typically contains more elements, for example v= {180, 181, 182,....,200}. • If the possible intensity values 0 to 255, v set could be any subset of these 256 values.
- 5. Relationship between pixels •Types of adjacency • 1. 4-adjacency: Two pixels p and q with values from v are 4-adjacent if q is in the set N4 (p). • 2. 8-adjacency: Two pixels p and q with values from v are 8-adjacent if q is in the set N8 (p). • 3. m-adjacency (mixed): two pixels p and q with values from v are m-adjacent if: – q is in N4 (p) or – q is in ND (P) and – The set N4 (p) ∩ N4 (q) has no pixel whose values are from v (No intersection).
- 6. Relationship between pixels •Mixed adjacency is a modification of 8-adjacency ''introduced to eliminate the ambiguities that often arise when 8- adjacency is used. (eliminate multiple path connection) • Pixel arrangement as shown in figure for v= {1}
- 7. Relationship between pixels •Path • A digital path (or curve) from pixel p with coordinate (x,y) to pixel q with coordinate (s,t) is a sequence of distinct pixels with coordinates (x0 , y0 ), (x1 , y1 ), ..., (xn , yn ) • where (x where (x0 0 , y , y0 0 ) = (x,y), (x ) = (x,y), (xn n , y , yn n )= (s,t) )= (s,t) • (xi , yi ) is adjacent pixel (xi-1 , yi -1) for 1≤j≤n , • n- The length of the path. • If (x0 , y0 ) = (xn , yn ):the path is closed path. • We can define 4- ,8- , or m-paths depending on the type of adjacency specified.
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- 13. Relationship between pixels •D4 distance
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