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# PIXELS RELATIONSHIP WITH NEIGHBOURS Notes | EduRev

Created by: Shalini Verma

## : PIXELS RELATIONSHIP WITH NEIGHBOURS Notes | EduRev

``` Page 1

Basic Relationships Between
Pixels
â€¢ Neighborhood
â€¢ Connectivity
â€¢ Paths
â€¢ Regions and boundaries
Page 2

Basic Relationships Between
Pixels
â€¢ Neighborhood
â€¢ Connectivity
â€¢ Paths
â€¢ Regions and boundaries
Neighbors of a Pixel
â€¢ Any pixel p(x, y) has two vertical and two
horizontal neighbors, given by
(x+1, y), (x-1, y), (x, y+1), (x, y-1)
â€¢ This set of pixels are called the 4-neighbors of
P, and is denoted by N
4
(P).
â€¢ Each of them are at a unit distance from P.
Page 3

Basic Relationships Between
Pixels
â€¢ Neighborhood
â€¢ Connectivity
â€¢ Paths
â€¢ Regions and boundaries
Neighbors of a Pixel
â€¢ Any pixel p(x, y) has two vertical and two
horizontal neighbors, given by
(x+1, y), (x-1, y), (x, y+1), (x, y-1)
â€¢ This set of pixels are called the 4-neighbors of
P, and is denoted by N
4
(P).
â€¢ Each of them are at a unit distance from P.
â€¢ The four diagonal neighbors of p(x,y) are
given by,
(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1 ,y-1)
â€¢ This set is denoted by N
D
(P).
â€¢ Each of them are at Euclidean distance of
1.414 from P.
Neighbors of a Pixel (Contd..)
Page 4

Basic Relationships Between
Pixels
â€¢ Neighborhood
â€¢ Connectivity
â€¢ Paths
â€¢ Regions and boundaries
Neighbors of a Pixel
â€¢ Any pixel p(x, y) has two vertical and two
horizontal neighbors, given by
(x+1, y), (x-1, y), (x, y+1), (x, y-1)
â€¢ This set of pixels are called the 4-neighbors of
P, and is denoted by N
4
(P).
â€¢ Each of them are at a unit distance from P.
â€¢ The four diagonal neighbors of p(x,y) are
given by,
(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1 ,y-1)
â€¢ This set is denoted by N
D
(P).
â€¢ Each of them are at Euclidean distance of
1.414 from P.
Neighbors of a Pixel (Contd..)
â€¢ The points N
D
(P) and N
4
(P) are
together known as 8-neighbors of the
point P, denoted by N
8
(P).
â€¢ Some of the points in the N
4
, N
D
and
N
8
may fall outside image when P lies
on the border of image.
Neighbors of a Pixel (Contd..)
Page 5

Basic Relationships Between
Pixels
â€¢ Neighborhood
â€¢ Connectivity
â€¢ Paths
â€¢ Regions and boundaries
Neighbors of a Pixel
â€¢ Any pixel p(x, y) has two vertical and two
horizontal neighbors, given by
(x+1, y), (x-1, y), (x, y+1), (x, y-1)
â€¢ This set of pixels are called the 4-neighbors of
P, and is denoted by N
4
(P).
â€¢ Each of them are at a unit distance from P.
â€¢ The four diagonal neighbors of p(x,y) are
given by,
(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1 ,y-1)
â€¢ This set is denoted by N
D
(P).
â€¢ Each of them are at Euclidean distance of
1.414 from P.
Neighbors of a Pixel (Contd..)
â€¢ The points N
D
(P) and N
4
(P) are
together known as 8-neighbors of the
point P, denoted by N
8
(P).
â€¢ Some of the points in the N
4
, N
D
and
N
8
may fall outside image when P lies
on the border of image.
Neighbors of a Pixel (Contd..)
Neighbors of a pixel
a. 4-neighbors of a pixel p
are its vertical and
horizontal neighbors
denoted by N
4
(p)
b. 8-neighbors of a pixel p
are its vertical
horizontal and 4
diagonal neighbors
denoted by N
8
(p)
p
N
4
(p)
p
N
8
(p)
Neighbors of a Pixel (Contd..)
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