Pixels in a digital image have spatial relationships where they are neighbors based on their location. Pixels that are horizontally, vertically, or diagonally adjacent are considered 8-neighbors of a pixel. Connectivity between pixels is important for determining boundaries and regions in an image, with adjacency defined based on similar pixel values. There are three types of pixel adjacency: 4-adjacency for horizontal and vertical neighbors only, 8-adjacency including diagonal neighbors, and mixed adjacency which can consider farther pixel relationships.

1. Basic relationship between
pixels

2. Basic relationship between pixels

4. If f(x,y) is on the border of the image, some of the neighbours of P lie
outside the digital image

5. Diagonal neighbors ND (P)

6. 8- Neighbors N8(P)
• The diagonal neighbors together with 4-neighbours are
called 8-neighbors of the pixel ‘p”. It is denoted by N8(P)

8. Connectivity / Adjacency
• Connectivity between pixels is important because it is used in
establishing boundaries of objects and components of region
in an image.
• The adjacency relationship is defined considering similar
pixels.
• Let {v} be the set of gray values from 0-255 which are used to
define adjacency.
• There are three types of adjacency
• 4- adjacency
• 8- adjacency
• M- adjacency or Mixed adjacency