Image Processing Reference
In-Depth Information
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Fig. 10.30. The images illustrate the direction tensor, represented as
I
20
(
left
)and
I
11
(
right
),
for Fig. 10.15 and computed by using theorem 10.4 and Eqs. (10.87)-(10.89). The hue encodes
the direction, whereas the brightness represents the magnitudes of the complex numbers. There
were 18 tune-on directions in the filter set
In this case, the Cartesian separability of the filters is not a serious advantage because
the grid is sparse and the spectral sampling can be done by simple scalar products
with Gabor filters.
10.15 Hough Transform of Lines
The Hough transform is a nonlinear filtering technique to estimate the position and
direction of certain curves in a discrete image [111]. Despite its name, it is not an
invertible transform in the sense of Fourier transform or the like.
The simplest Hough transform is the
Hough transform of lines
. It detects (in-
finitely) long lines, which we discuss in this section. To find lines, it can be imagined
that a gradient filtering would be sufficient. Even in an ideal image free of noise,
significantly large segments of lines may be missing for a variety of reasons. For
example, lines of an object may be occluded because another object is in front of it.
The Hough transform does not replace gradient filtering but starts from the result of
it, to be precise the gradient image to the magnitude of which a threshold has been
applied, to group together the scattered segments of the same line. A summary of the
Hough transform for lines is given next.
1. The curve family of lines is modeled and parameterized. Because of its unbiased
properties w.r.t. directions, one commonly used line model is:
k
T
r
=cos(
φ
)
·
x
+sin(
φ
)
·
y
=
b
(10.91)
Here
φ
and
b
are the parameters representing the direction and the closest dis-
tance of the line to the origin, marked between the points
O
and
B
in Fig. 10.33.
