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4/28/2008
1
Pixel Relationships
84
()
D
Np
N
p
N
p
=
∪
N
D
(
p
)
1
copyright 2002©H. R. Myler
A pixel has four horizontal
and vertical neighbors
and four diagonal neighbors
Some of the neighbors may fall outside the image if
p
is on
the border of the image
mConnectivity
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
4connected
8connected
mconnected
0
1
0
0
0
1
V
– set of intensity values used to define connectivity. In binary
images,
V
= {1} – refers to connectivity of pixels with value 1.
2
copyright 2002©H. R. Myler
Two pixels, p and q, with values from
V
are
mconnected
if:
(i) q is in N
4
(p)
or
(ii) q is in N
D
(p) and N
4
(p)
∩
N
4
(q) is empty.
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2
A (digital) path (or curve) from pixel
p
with coordinates
(x,y) to pixel
q
with coordinates (s,t) is a sequence of
distinct pixels with coordinates
00
11
(
,
), ( ,
),.
..(
,
)
nn
x
yx
y
x
y
where
()
(
)
(
)
xy
xya
n
dxy
s
t
(
,)( ,
)(
, )( , )
=
=
and pixels
(, )
( , )
ii
i
i
x
y and x
y
+
+
are connected for
1
in
≤
≤
In this case,
n
is the length of the path.
If
(, )(, )
x
y
=
the path is a closed path.
We can define 4, 8, or mpaths depending on type of
3
copyright 2002©H. R. Myler
connectivity specified: path between top right and
bottom right pixels are 8—paths and mpath (previous
slide)
If S is a subset of pixels in am image, two pixels
p
and
q
are said to be connected in S if there is a path between
them consisting entirely of pixels in S.
For any
p
in S the set of pixels that are connected to it in
For any
in S, the set of pixels that are connected to it in
S is called a
connected component
of S. if it only has
one connected component, then set S is called a
connected set
.
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