Image Processing Reference
In-Depth Information
4.4.1 Commencing a Straight Edge
We visit each point of the image in row-major order, and compute its Pre-
witt response [92]. If the (Prewitt) response at a point p exceeds the threshold
value, T (= 100 in our experiments), and the response is a local maximum in
N
8
(p) (i.e., the response of each 8-neighbor of p does not exceed that of p),
then p is a start point, namely p
s
(i
s
,j
s
). The next point on the edge commenc-
ing from p
s
is obtained from the responses in N
8
(p
s
). The direction d
s
from
p
s
is the chain code from p
s
to its neighbor having the maximum response. In
case of multiple maxima (which indicates multiple edges incident at p
s
), we
consider each of them, one by one, to find the straight edges from p
s
.
To get the (straight-)edge point next to the current point p, we need not
apply the convolution at each neighbor of p with the Prewitt operator (in
order to get their responses, and the maximum/maxima, thereof). Instead, in
our algorithm, checking the Prewitt responses at three neighbors correspond-
ing to three directions su
ces: d, (d+ 1)(mod 8), and (d+ 7)(mod 8), where d
is the chain code of p. It may be noted that, by dint of Property R1, no other
neighbor can be the next point on the current edge. Hence, out of the three
possible neighbors, we select the one having the maximum response as the
next point, provided its response is greater than T (in case of multiple max-
ima, we consider each, as explained earlier). Further, to capture the previous
information as a part of the predicted direction, we have taken the exponential
average of Prewitt responses, as explained next.
4.4.2 Exponential Averaging
It is a quick and effective method, as shown in [168], to estimate the edge
strength at an edge point using its own response and the weighted contribution
of responses at the previous edge points. In order to compute the exponen-
tial average of the response at a point p, we need to consider the responses
that have already been computed and stored—at the previous points up the
straight edge. In an 8-bit image, since the maximum possible (Prewitt) re-
sponse at a point p is 3×256, and since an exponentially decreasing factor of
1
2
for the contributing points up the edge is taken, eight previous responses are
enough to compute the exponential average at p. Hence, the average response
at p is given as follows:
R
E
=
R
P
+
2
R
(−1)
2
2
R
(−2)
2
8
R
(−8)
1
1
+
+ ... +
E
E
E
(4.16)
1+
2
+
1
1
2
8
2
2
+ ... +
where R
(−i
E
(1 6 i 6 8) denotes the exponentially averaged response at the
ith previous point, R
P
denotes the (Prewitt-operator-based) response at the
current point p, and R
E
is the exponentially averaged response at p. Such
a strategy gives a boost to p to be an edge point when it shows a weak
response R
P
(possibly due to noise) but lies on the edge. If the point p that
lies on the edge but has weak response is not taken into consideration, then
