Master thesis: Stereo Vision with Conical and Circular Features
Thesis by: Veselin Dikov
Advisor: Nassir Navab
Supervision by: Nassir Navab
Due date: finished
Abstract
The topic of this master thesis is stereo vision with conical (elliptical) and circular features.
Stereo vision is a major subject in the scientific field of computer vision. The main task
in stereo vision is the 3D reconstruction of a scene given images of the scene taken by two
cameras. But first, the geometrical relations between both cameras, represented by the so
called epipolar geometry, need to be found. The traditional algorithms that estimate the
epipolar geometry between two images are based on point image features.
Ellipses and circles as image features have certain advantages compared to point features:
they can be extracted more easily and with higher accuracy from the image, even when they
are partially occluded, and they can be identified more easily in multiple images. Such features
can be found in many man-made objects, even if point features are completely missing. It is
theoretically proven that four conical features in general position are enough for estimation
of the epipolar geometry, but, unfortunately, not in a linear manner.
Innovative ideas for handling linearly this estimation problem for certain specific cases
are developed in this thesis. We propose an algorithm, which finds groups of ellipses that lie
on one and the same plane in space. Based on the results of this algorithm, we develop linear
methods for estimating the epipolar geometry. We show that the minimal configuration of
three ellipses suffices, given that two of the ellipses lie on one plane. Furthermore, we show
that the epipolar geometry can be computed from two circles on one plane. For this we
deploy selfcalibration methods, which were not used in combination with binocular stereo
vision so far. In the case when the cameras are known ( i.e. their parameters like focal length
and relative position) we show that two coplanar ellipses or two circles in general position
are also sufficient.
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