Relationships between pixels(Neighbours and Connectivity)
An image is denoted by f(x,y) and p,q are used to represent individual pixels of the image.
Neighbours of a pixel
A pixel p at (x,y) has 4-horizontal/vertical neighbours at (x+1,y), (x-1,y), (x,y+1) and (x,y-1). These are called the 4-neighbours of p : N4(p).
A pixel p at (x,y) has 4 diagonal neighbours at (x+1,y+1), (x+1,y-1), (x-1,y+1) and (x-1,y-1). These are called the diagonal-neighbours of p : ND(p).
The 4-neighbours and the diagonal neighbours of p are called 8-neighbours of p : N8(p).
Adjacency between pixels
Let V be the set of intensity values used to define adjacency.
In a binary image, V ={1} if we are referring to adjacency of pixels with value 1. In a gray-scale image, the idea is the same, but set V typically contains more elements.
For example, in the adjacency of pixels with a range of possible intensity values 0 to 255, set V could be any subset of these 256 values.
We consider three types of adjacency:
a) 4-adjacency: Two pixels p and q with values from V are 4-adjacent if q is in the set N4(p).
b) 8-adjacency: Two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).
c) m-adjacency(mixed adjacency): Two pixels p and q with values from V are m-adjacent if
- q is in N4(p), or
- 2) q is in ND(p) and the set N4(p)∩N4(q) has no pixels whose values are from V.
Connectivity between pixels
It is an important concept in digital image processing.
It is used for establishing boundaries of objects and components of regions in an image.
Two pixels are said to be connected:
- if they are adjacent in some sense(neighbour pixels,4/8/m-adjacency)
- if their gray levels satisfy a specified criterion of similarity(equal intensity level)
There are three types of connectivity on the basis of adjacency. They are:
a) 4-connectivity: Two or more pixels are said to be 4-connected if they are 4-adjacent with each others.
b) 8-connectivity: Two or more pixels are said to be 8-connected if they are 8-adjacent with each others.
c) m-connectivity: Two or more pixels are said to be m-connected if they are m-adjacent with each others.
References:
[1] Digital Image processing 3rd edition, Rafael C. Gonzalez & Richard E. Woods
