Image Processing Reference
In-Depth Information
grid lines
E
i
V
ij
P
ik
P
ij
H
ij
= H
ik
V
ik
S
i
FIGURE 4.5: Isothetic distance of P
ij
(from S
i
E
i
) is P
ij
V
ij
, which is greater
than
2
, thereby making P
ij
an error point, whereas, P
ik
is not an error point,
since the isothetic distance of P
ik
is P
ik
V
ik
, which is less than
2
.
4.2.3 Error Points
An ADSS extracted from an input digital curve segment may not be a
perfect DSS. There may occur erroneous points. An erroneous point or error
point is one whose isothetic distance (i.e., minimum of the vertical distance
and the horizontal distance) from the real straight line corresponding to the
concerned ADSS is greater than 1/2. To check whether a point is an error
point or not, we use Eq. 4.9, stated as follows.
Let S
i
and E
i
be the start point and the end point of the ith ADSS, and
let P
ij
be the jth digital point on the ith ADSS, as shown in Fig. 4.5. Let
S
i
E
i
denote the real line segment joining S
i
and E
i
. Then it can be shown
that P
ij
= (x
p
,y
p
) is an error point corresponding to the line S
i
E
i
, if and only
if
|}> 0, (4.9)
where, x
ES
= x
e
− x
s
, y
ES
= y
e
− y
s
, etc. Note that (x
s
,y
s
) and (x
e
,y
e
)
denote the respective coordinates of the start point and the end point of the
ADSS under consideration. Although Eq. 4.9 is not required at any stage in
our algorithm, it enables us to check whether or not P
ij
is an error point
without using any floating point arithmetic.
2|x
ES
y
EP
−x
EP
y
ES
|−max{|x
ES
|,|y
ES
4.3 Polygonal Approximation
Extraction of the ADSS for each curve C
k
in the given set (binary image)
I = {C
k
}
k=1
of digital curves generates an ordered set of ADSS, namely,
A
k
= L
(k)
n
k
i=1
, corresponding to C
k
. In each such set A
k
, several consecutive
i
