Image Processing Reference
In-Depth Information
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(a) Image containing a circle
(b) Accumulator space
r
Circles of
votes
Original
circle
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(c) 3D accumulator space
Figure 5.10
Illustrating the Hough transform for circles
sparse coverage. The accumulator space,
acc
(initially zero), is incremented only for
points whose co-ordinates lie within the specified range (in this case the centre cannot lie
outside the original image).
The application of the HT for circles is illustrated in Figure
5.11
. Figure
5.11
(a) shows
an image with a synthetic circle. In this figure, the edges are complete and well defined.
The result of the HT process is shown in Figure
5.11
(d). The peak of the accumulator space
is at the centre of the circle. Note that votes exist away from the circle's centre, and rise
towards the locus of the actual circle, though these background votes are much less than
the actual peak. Figure
5.11
(b) shows an example of data containing occlusion and noise.
The image in Figure
5.11
(c) corresponds to the same scene, but the noise level has been
increased by changing the threshold value in the edge detection process. The accumulators
for these two images are shown in Figures
5.11
(e) and
5.11
(f) and the circles related to the
parameter space peaks are superimposed (in black) on the edge images in Figures
5.11
(g)
