Discrete-time signal processing
Discrete-time signal processing
Introduction to theoretical kinematics
Introduction to theoretical kinematics
Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics
Generalized homogeneous coordinates for computational geometry
Geometric computing with Clifford algebras
Signal Processing for Computer Vision
Signal Processing for Computer Vision
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Algebraic Aspects of Designing Behaviour Based Systems
AFPAC '97 Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle
Surface Evolution and Representation using Geometric Algebra
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Practical parameterization of rotations using the exponential map
Journal of Graphics Tools
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
Fourier Preprocessing for Hand Print Character Recognition
IEEE Transactions on Computers
Fourier Descriptors for Plane Closed Curves
IEEE Transactions on Computers
IEEE Transactions on Signal Processing
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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 ℝ4,1 of the Euclidean space ℝ3. 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.