Image Processing Reference
In-Depth Information
Also, we might know brightness information: the pupil is darker than the surrounding iris.
These factors can be formulated as constraints on whether edge points can vote within the
accumulator array. A simple modification is to make the votes proportional to edge magnitude,
in this manner, points with high contrast will generate more votes and hence have more
significance in the voting process. In this way, the feature extracted by the HT can be
arranged to suit a particular application.
(a) Image of eye
(b) Sobel edges
(c) Edges with HT detected circle
Figure 5.12
Using the HT for circles
5.4.4
HT for ellipses
Circles are very important in shape detection since many objects have a circular shape.
However, because of the camera's viewpoint, circles do not always look like circles in
images. Images are formed by mapping a shape in 3D space into a plane (the image plane).
This mapping performs a perspective transformation. In this process, a circle is deformed
to look like an ellipse. We can define the mapping between the circle and an ellipse by a
similarity transformation. That is,
S
S
t
t
x
y
cos(
)
sin(
)
x
y
x
x
=
+
(5.33)
- sin(
)
cos(
)
y
y
where ( x
, y
) define the co-ordinates of the circle in Equation 5.31,
represents the
orientation, ( S x , S y ) a scale factor and ( t x , t y ) a translation. If we define
a 0 = t x
a x = S x cos(
)
b x = S y sin(
)
(5.34)
b 0 = t y
a y = - S x sin(
)
b y = S y cos(
)
then we have that the circle is deformed into
x = a 0 + a x cos(
) + b x sin(
)
(5.35)
)
This equation corresponds to the polar representation of an ellipse. This polar form contains
six parameters ( a 0 , b 0 , a x , b x , a y , b y ) that characterise the shape of the ellipse.
y = b 0 + a y cos (
) + b y sin(
is not a free
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