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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Twists – An Operational Representation of Shape
verfasst von : Gerald Sommer, Bodo Rosenhahn, Christian Perwass
Erschienen in: Computer Algebra and Geometric Algebra with Applications
Verlag: Springer Berlin Heidelberg
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We give a contribution to the representation problem of free-form curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group
SE
(3). While in Euclidean space the modelling of shape as an orbit of a point under the action of
SE
(3) is limited, we are embedding our problem into the conformal geometric algebra ℝ
4,1
of the Euclidean space ℝ
3
. This embedding results in a number of advantages which makes the proposed method a universal and flexible one with respect to applications. It makes possible the robust and fast estimation of the pose of 3D objects from incomplete and noisy image data. Especially advantagous is the equivalence of the proposed shape model to that of the Fourier representations.