A Simple Image Formation Model

$$ f(x, y) = i(x,y)r(x,y) $$

• $f(x,y)$: 2D digital image
• $i(x, y)$: illumination
• $r(x, y)$: reflection
  • $0<r(x, y)<1$

Some Basic Relationships Between Pixels

• $N_4(p)$: 4-neighbors of $p$
  • $p=(x, y)$
  • $(x+1, y), (x-1, y), (x, y+1), (x, y-1)$
• $N_D(p)$: diagonal neighbors of $p$
  • $p=(x, y)$
  • $(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1)$
• $N_8(p)$: union of $N_4(p)$ and $N_D(p)$

Distance Measures

• Euclidean distance
  • $D_e(p, q) = \sqrt{(x-s)^2+(y-t)^2}$
• $D_4$ distance (city-block distance)
  • $D_4(p, q) = |x-s| + |y-t|$
• $D_8$ distance (chessboard distance)
  • $D_8(p, q) = \max(|x-s|, |y-t|)$