improve the efﬁciency of the method by multistarting
the method.
4.1 Real-world Problems
The proposed method for solving the multiple ellipse
detection problem can also be applied to real images.
For that purpose, we carried out the preprocessing of
the edge detection by using the Canny ﬁlter ﬁrst (see
Bradski (2000); Wolfram Research (2016)).
In Fig 5a a fetal head detection on an ultrasound
image is shown. Corresponding edge curves obtained
by Canny ﬁlter in Fig 5b are shown. The red ellipse
in Fig 5a denotes the fetal head. Similarly, in Fig 6,
a detection problem for several cups on the table is
considered.
(a) Detection (b) Canny ﬁlter
Figure 5: Real image.
(a) Detection (b) Canny ﬁlter
Figure 6: Real image.
5 CONCLUSIONS
Solving multiple ellipse detection problem is impor-
tant in many applications. In our paper one and mul-
tiple ellipse detection problem are considered on the
basis of a data point set coming from a number of el-
lipses with noisy edges in the plane. Thereby, we sup-
pose that the subset of data points coming from some
ellipse satisﬁes the “homogeneity property”. For that
situation, a method based on the RANSAC-method is
proposed, whereby the DBSCAN-parameters MinPts
and ε play a signiﬁcantly important role.
It is important to note that the RM-algorithm
does not require the use of indexes for recognizing
the most appropriate partition with ellipse-cluster-
centers. This is the basic advantage of this method
regarding the method EDCircles given in (Akinlar
and Topal, 2013) and method given in (Grbi
´
c et al.,
2016). Unlike our method, EDCircles does not rec-
ognize an ellipse with semi-axes (ξ, η),
ξ
η
≥ 4 and
cannot detect a single ellipse with a clear edge if
its shape departs signiﬁcantly from a circular shape.
However, our method requires more computing time
than EDCircles.
The method proposed in our paper could be ap-
plied to the case of other geometrical objects too, but
its application is also possible in 3D.
ACKNOWLEDGEMENTS
The author would like to thank the referees and the
journal editors for their careful reading of the pa-
per and insightful comments that helped us improve
the paper. Especially, the author would like to thank
Mrs. Katarina Mor
ˇ
zan for signiﬁcantly improving the
use of English in the paper. This work was supported
by the Croatian Science Foundation through research
grants IP-2016-06-6545 and IP-2016-06-8350.
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