Q3Digital Image Processing

A pixel $p$ at coordinates $(x,y)$ has four horizontal/vertical neighbors, $N_4(p)$, at $(x+1,y),(x-1,y),(x,y+1),(x,y-1)$, and four diagonal neighbors, $N_D(p)$, at $(x+1,y+1),(x+1,y-1),(x-1,y+1),(x-1,y-1)$. The union of these eight gives the 8-neighbors, $N_8(p)$. Adjacency requires two pixels to be neighbors and to satisfy some intensity similarity criterion; 4-adjacency, 8-adjacency, and m-adjacency (mixed, used to remove ambiguity in 8-adjacency paths) build on this. Connectivity extends adjacency along a path of pixels to define regions, while distance measures such as Euclidean, City-block ($D_4$), and Chessboard ($D_8$) distance quantify separation between pixels.