4-connectivity and 8-connectivity of components


A pixel is 4-connected to another
pixel if they share an adjacent 
vertical or horizontal side.


   Image[i,j] is 4 connected
   to the pixels 
        Image[i+1, j],
        Image[i-1, j], 
        Image[i, j+1],
        Image[i, j-1]
         
A pixel is 8-connected to another
pixel if they share an adjacent ver-
tical or horizontal side OR a diagonal
adjacency.

   Image[i,j] is 8 connected
   to the pixels 
        Image[i+1,j], Image[i-1,j] 
        Image[i,j+1], Image[i,j-1]
        Image[i+1,j+1], Image[i+1,j-1] 
        Image[i-1,j+1], Image[i-1,j-1]
      
 A binary image example:

  0  1  0  0  0  0  0  0 
  0  1  1  0  0  0  0  0 
  0  0  0  1  0  0  0  0
  0  0  0  0  1  1  1  0  
  0  0  0  0  1  0  1  0
  1  1  1  0  1  1  1  0
  0  1  1  0  0  0  0  0
  0  0  0  0  0  0  0  0

Another binary image:

  0  1  0  0  0  1  1  1
  0  1  1  0  0  0  1  0
  0  0  0  1  0  0  0  0
  0  0  0  0  1  1  1  0
  0  0  0  0  1  0  1  0 
  1  1  1  0  1  1  1  0
  0  1  1  0  0  0  0  0
  0  0  0  0  0  0  1  0
 

The binary image converted to
labeled "4-connected" components:

  0  1  0  0  0  0  0  0
  0  1  1  0  0  0  0  0
  0  0  0  2  0  0  0  0
  0  0  0  0  3  3  3  0
  0  0  0  0  3  0  3  0
  4  4  4  0  3  3  3  0
  0  4  4  0  0  0  0  0
  0  0  0  0  0  0  0  0
     
The image converted to labeled
"8-connected" components:

   0  1  0  0  0  2  2  2
   0  1  1  0  0  0  2  0
   0  0  0  1  0  0  0  0
   0  0  0  0  1  1  1  0
   0  0  0  0  1  0  1  0
   3  3  3  0  1  1  1  0 
   0  3  3  0  0  0  0  0
   0  0  0  0  0  0  4  0