Image Processing Toolbox

4- and 8-Connected Neighborhoods

For many operations, distinguishing objects depends on the convention used to decide whether pixels are connected. There are two different conventions typically used: 4-connected or 8-connected neighborhoods.

In an 8-connected neighborhood, all of the pixels that touch the pixel of interest are considered, including those on the diagonals. This means that if two adjoining pixels are on, they are part of the same object, regardless of whether they are connected along the horizontal, vertical, or diagonal direction.

Figure 9-4: An 8-Connected Neighborhood

In a 4-connected neighborhood, the pixels along the diagonals are not considered. This means that a pair of adjoining pixels are part of the same object only if they are both on and are connected along the horizontal or vertical direction.

Figure 9-5: A 4-Connected Neighborhood

The type of neighborhood you choose affects the number of objects found in an image and the boundaries of those objects. Therefore, the results of the object-based operations often differ for the two types of neighborhoods.

For example, this matrix represents a binary image that has one 8-connected object or two 4-connected objects.

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

Object-Based Operations

Perimeter Determination