A HIERARCHICAL 3D CIRCLE DETECTION ALGORITHM
APPLIED IN A GRASPING SCENARIO
Emre Bas¸eski, Dirk Kraft and Norbert Kr
¨
uger
The Maersk Mc-Kinney Moller Institute, University of Southern Denmark
Campusvej 55 DK-5230 Odense M, Odense, Denmark
Keywords:
3D circle detection, Grasping, Stereo vision, Hierarchical representation.
Abstract:
In this work, we address the problem of 3D circle detection in a hierarchical representation which contains
2D and 3D information in the form of multi-modal primitives and their perceptual organizations in terms of
contours. Semantic reasoning on higher levels leads to hypotheses that then become veriﬁed on lower levels by
feedback mechanisms. The effects of uncertainties in visually extracted 3D information can be minimized by
detecting a shape in 2D and calculating its dimensions and location in 3D. Therefore, we use the fact that the
perspective projection of a circle on the image plane is an ellipse and we create 3D circle hypotheses from 2D
ellipses and the planes that they lie on. Afterwards, these hypotheses are veriﬁed in 2D, where the orientation
and location information is more reliable than in 3D. For evaluation purposes, the algorithm is applied in a
robotics application for grasping cylindrical objects.
1 INTRODUCTION
Circles are important structures in machine vision
since they are a common feature for natural and
human-made objects and they provide more informa-
tion than points and lines about the pose of an ob-
ject. In 3D vision, there are various ways of obtain-
ing edge-like 3D entities (sparse stereo) from a stereo
camera setup. Once the sparse stereo data is grouped
with respect to a perceptual organization scheme, cer-
tain structures can be extracted from individual or
combinations of these perceptual groups. Both, in
dense and sparse stereo the correspondence ﬁnding
phase in 3D reconstruction reduces the reliability of
the information. Therefore, while detecting a certain
structure like a 3D circle by using this kind of infor-
mation, one needs to take into account the noise and
uncertainty of the information.
The algorithms that are used to detect 3D circles
can be grouped into three categories. The ﬁrst cat-
egory consists of voting algorithms like the Hough
transform (Duda et al., 2000). Due to the size of
the parameter space, voting algorithms require much
more memory and computational power than other al-
gorithms.
The second category contains analytical algo-
rithms which use the geometric properties of circles
(e.g., (Xavier et al., 2005)). For laser-range data, this
kind of algorithms run fast and are robust because of
the high-reliability of input data. Stereo vision on the
other hand, introduces too many outliers and uncer-
tainties that make the geometrical properties unstable.
The last category involves ﬁtting algorithms. They
are traditionally based on minimizing a cost func-
tion which depends on a distance function that mea-
sures errors between given points and the ﬁtted circle
(Jiang and Cheng, 2005; Chernov and Lesort, 2005;
Shakarji, 1998). The ﬁtting process can be done ei-
ther in 3D or in 2D. If it is done in 2D, the optimal
plane for the given points is calculated and the points
are projected onto that plane. If the ﬁtting is done
in 3D, the minimization starts with an initial estimate
and tries to converge to the optimal circle. However,
to guarantee convergence, a good initialization is re-
quired. This can be done by starting with multiple
initializations, which decreases the computational ef-
ﬁciency drastically. One can reduce the parameter
space as in (Jiang and Cheng, 2005) but the noisy na-
ture of stereo vision data decreases the probability of
convergence. Therefore, although ﬁtting in 2D is a
decoupled solution (plane ﬁtting and curve ﬁtting are
handled separately), it is more advantageous in terms
of efﬁciency and reliability for noisy data.
In this article, an algorithm which is based on ﬁt-
ting in 2D is presented. Note that, the common prac-
tice for such approaches is using only 3D information
496
Baseski E., Kraft D. and Kruger N. (2009).
A HIERARCHICAL 3D CIRCLE DETECTION ALGORITHM APPLIED IN A GRASPING SCENARIO.
In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 496-502
DOI: 10.5220/0001796004960502
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