neighbouhood cells
Post on 07-Apr-2018
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Basic Relationships Between
Pixels
Neighborhood
Adjacency Connectivity
Paths Regions and boundaries
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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)
This set is denoted by ND(P).
Each of them are at Euclidean distance of
1.414 from P.
Neighbors of a Pixel (Contd..)
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Neighbors of a pixel
a. 4-neighbors of a pixel pare its vertical and
horizontal neighbors
denoted by N4(p)b. 8-neighbors of a pixel p
are its vertical
horizontal and 4diagonal neighbors
denoted by N8(p)
pN4(p)
p
N8(p)
Neighbors of a Pixel (Contd..)
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Neighbors of a Pixel (Contd..)
ND N4 ND
N4 P N4
ND N4 ND
N4 - 4-neighborsND - diagonal neighbors
N8 - 8-neighbors (N4 U ND)
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Adjacency
Two pixels are connected if they are
neighbors and their gray levels satisfysome specified criterion of similarity.
For example, in a binary image two pixels
are connected if they are 4-neighbors and
have same value (0/1).
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Connectivity :
To determine whether the pixelsare adjacent in some sense.
Let V be the set of gray-levelvalues used to define connectivity;
then Two pixels p, q that have values
from the set V are:
a. 4-connected, if q is in the set N4(p)
b. 8-connected, if q is in the set N8(p)
c. m-connected, iff
i. q is in N4(p) or
ii. q is in ND(p) and the set
is empty
0 1 1
0 2 0
0 0 1
0 1 1
0 2 0
0 0 1
a.
b.
c.
V = {1, 2}
)()(44
qNpN I
0 1 1
0 2 0
0 0 1
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Adjacency/Connectivity
0 1 1
0 1 0
0 0 1
8-adjacent
m-adjacent
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Pixel p is adjacentto pixel q if they are connected.
Two image subsets S1 and S2 are adjacent if somepixel in S1 is adjacent to some pixel in S2
Adjacency/Connectivity
S1
S2
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Paths & Path lengths
Apath from pixel p with coordinates(x, y) to pixel q with coordinates (s, t)
is a sequence of distinct pixels withcoordinates:
(x0, y0), (x1, y1), (x2, y2) (xn, yn),
where (x0, y0)=(x, y) and (xn, yn)=(s, t);(xi, yi) is adjacent to (xi-1, yi-1)
Here n is the length of the path.
We can define 4-, 8-, and m-paths basedon type of adjacency used.
ni 1
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Connected Components
Ifp and q are pixels of an image subset S
thenp isconnectedto q in S if there is a
path fromp to q consisting entirely of
pixels in S.
For every pixelp in S, the set of pixels inS that are connected top is called a
connected component of S. If S has only one connected component
then S is called Connected Set.
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Regions and Boundaries
A subset R of pixels in an image is
called aRegion of the image if R is aconnected set.
The boundary of the region R is theset of pixels in the region that haveone or more neighbors that are notin R.
If R happens to be entire Image?
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Distance measures
Given pixelsp, q and zwith coordinates
(x, y), (s, t), (u, v) respectively, the distancefunction D has following properties:
a. D(p, q) 0[D(p, q) = 0, iff p = q]
b. D(p, q) = D(q, p)
c. D(p, z) D(p, q) + D(q, z)
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The follow ing are the different
Distance measures:
Euclidean Distance :
De( p , q ) = [ ( x - s)2
+ ( y - t )2
]
b. City Block Distance: D4( p , q ) = | x -s| + | y - t |
c. Chess Board Distance: D8( p , q ) = m ax ( | x -s| , | y - t | )
22222
21112
21012
21112
22222
2
212
21012212
2
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Relationship between pixels (Contd..)
Arithmetic/Logic Operations:- Addition : p + q
Subtraction: p q
Multiplication: p * q
Division: p / q
AND: p AND q
OR : p OR q
Complement: NOT(q)
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Arithmetic/Logic Operations
Tasks done using neighborhoodprocessing:
Smoothing / averaging
Noise removal / filtering
Edge detection
Contrast enhancement
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END o f Ne ighb or ho od
and Con nect i v i t y
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