Image Processing Reference
In-Depth Information
600
600
500
500
400
400
300
300
200
200
100
100
0
0
0
50
100
150
200
250
0
50
100
150
(a) Accumulators for Figure 5.7(a)
150
2000
1500
100
1000
50
500
0
0
0
50
100
150
0
50
100
150
200
250
300
(b) Accumulators for Figure 5.7(b)
Figure 5.15
Parameter space reduction for the Hough transform for lines
()
1
0
+ ( )
0
() =
x
y
1
(5.43b)
where
x
(
) = -
r
sin(
)
y
(
) =
r
cos(
)
(5.44)
)
Figure
5.16
illustrates the definition of the first and second directional derivatives. The
first derivative defines a tangential vector while the second one is similar to the vector
function, but it has reverse direction. In fact, that the edge direction measured for circles
can be arranged so as to point towards the centre was actually the basis of one of the early
approaches to reducing the computational load of the HT for circles (Kimme, 1975).
According to Equation 5.42 and Equation 5.44, we observe that the tangent of the angle
of the first directional derivative denoted as
x
(
) = -
r
cos (
)
y
(
) = -
r
sin(
(
) is given by
