Neighbors of Pixel

There are two different ways to define the neighbors of a pixel $p$ located at $(x,y)$:

• 4-neighbors

  The 4-neighbors of pixel p, denoted by $N_4(p)$, are the four pixels located at $(x-1,y)$, $(x+1,y)$, $(x,y-1)$, and $(x,y+1)$, there are, respectively, above (north), below (south), to the left (west) and right (east) of the pixel p.

• 8-neighbors

  The 8-neighbors of pixel p, denoted by $N_8(p)$, include the four 4-neighbors and four pixels along the diagonal direction located at $(x-1,y-1)$ (northwest), $(x-1,y+1)$ (northeast), $(x+1,y-1)$ (southwest) and $(x+1,y+1)$ (southeast).