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要旨:
In this article we discuss the 2D-3D pose estimation problem of 3D free-form
contours. In our scenario we observe objects of any 3D shape in an image of a
calibrated camera. Pose estimation means to estimate the relative position and
orientation (containing a rotation and translation) of the 3D object to the
reference camera system. The fusion of modeling free-form contours within the
pose estimation problem is achieved by using the conformal geometric algebra.
The conformal geometric algebra is a geometric algebra which models entities as
stereographically projected entities in a homogeneous model. This leads to a
linear description of kinematics on the one hand and projective geometry on the
other hand. To model free-form contours in the conformal framework we use
twists to model cycloidal curves as twist-depending functions and interpret
n-times nested twist generated curves as functions generated by 3D Fourier
descriptors. This means, we use the twist concept to apply a spectral domain
representation of 3D contours within the pose estimation problem. We will show
that twist representations of objects can be numerically efficient and easily
be applied to the pose estimation problem. The pose problem itself is
formalized as implicit problem and we gain constraint equations, which have to
be fulfilled with respect to the unknown rigid body motion. Several experiments
visualize the robustness and real-time performance of our algorithms.
