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Pose estimation in conformal geometric algebra. Part II: Realtime pose estimation using extended feature concepts
 Journal of Mathematical Imaging and Vision
, 2005
"... Abstract. 2D3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D3D pose estimation problem: We discuss the involved mathematical spaces and their in ..."
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Cited by 21 (15 self)
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Abstract. 2D3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D3D pose estimation problem: We discuss the involved mathematical spaces and their interaction within higher order entities. To cope with the pose problem (how to compare 2D projective image features with 3D Euclidean object features), the principle we propose is to reconstruct image features (e.g. points or lines) to one dimensional higher entities
Monocular Pose Estimation of Kinematic Chains
 Applications of Geometric Algebra in Computer Science and Engineering
, 2002
"... ABSTRACT In this paper conformal geometric algebra is used to formalize an algebraic embedding for the problem of monocular pose estimation of kinematic chains. The problem is modeled on the base of several geometric constraint equations. In conformal geometric algebra the resulting equations are co ..."
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Cited by 12 (6 self)
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ABSTRACT In this paper conformal geometric algebra is used to formalize an algebraic embedding for the problem of monocular pose estimation of kinematic chains. The problem is modeled on the base of several geometric constraint equations. In conformal geometric algebra the resulting equations are compact and clear. To solve the equations we linearize and iterate the equations to approximate the pose and the kinematic chain parameters. 1.1
Tracking with a Novel Pose Estimation Algorithm
 International Workshop on Robot Vision
, 2001
"... In this paper we apply a novel pose estimation algorithm to the tracking problem. We make use of error measures of the algorithm which enable us to characterize the quality of an estimated pose. The key idea of the tracking algorithm is random start local search. The principle of the heuristic r ..."
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Cited by 10 (6 self)
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In this paper we apply a novel pose estimation algorithm to the tracking problem. We make use of error measures of the algorithm which enable us to characterize the quality of an estimated pose. The key idea of the tracking algorithm is random start local search. The principle of the heuristic relies upon a combination of iterative improvement and random sampling. While in many approaches a manually designed object representation is assumed, we overcome this condition by using accumulated object representations and combine these successfully with the tracking algorithm.
Pose Estimation of 3D Freeform Contours in Conformal Geometry
"... In this article we discuss the 2D3D pose estimation prob lem of 3D freeform contours. In our scenario we observe objects of any 3D shape in an image of a calibrated cam era. Pose estimation means to estimate the relative posi tion and orientation (containing a rotation R and translation vector ..."
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Cited by 1 (1 self)
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In this article we discuss the 2D3D pose estimation prob lem of 3D freeform contours. In our scenario we observe objects of any 3D shape in an image of a calibrated cam era. Pose estimation means to estimate the relative posi tion and orientation (containing a rotation R and translation vector t) of the 3D object to the reference camera system. The fusion of modeling freeform contours within the pose estimation problem is achieved by using the conformal geometric algebra. Freeform contours are modeled as 3D Fourier descriptors and combined with an ICP (Iterative Closest Point) algorithm they are embedded in the pose problem as unique entities. In this work we further concen trate on modeling multiple object contours (coming along with object occlusions, etc.) and the modeling of object deformations. Object deformations are achieved by combining kinematic chains within Fourier descriptors.
Pose Estimation of Cycloidal Curves by using Twist Representations
"... This work concerns the 2D3D pose estimation problem of cycloidal curves. Pose estimation means to estimate the relative position and orientation of a 3D object to a reference camera system. The 3D object features are in this work cycloidal curves, as extensions to classical 3D point or 3D line con ..."
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Cited by 1 (1 self)
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This work concerns the 2D3D pose estimation problem of cycloidal curves. Pose estimation means to estimate the relative position and orientation of a 3D object to a reference camera system. The 3D object features are in this work cycloidal curves, as extensions to classical 3D point or 3D line concepts. This means, we assume knowledge of a 3D cycloidal curve and observe it in an image of a calibrated camera. The aim is to estimate the rotation R and translation t to get a best fit of the transformed 3D object model to the observed 2D image data. Furthermore, other concepts such as 3D cycloidal surfaces and the numerical problems of estimating the pose parameters are discussed.
© 2003 SpringerVerlag New York Inc. FreeForm Pose Estimation by Using Twist Representations 1
"... Abstract. In this article we discuss the 2D–3D pose estimation problem of 3D freeform contours. We observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means estimating the relative position and orientation of the 3D object to the reference camera system. While cycloi ..."
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Abstract. In this article we discuss the 2D–3D pose estimation problem of 3D freeform contours. We observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means estimating the relative position and orientation of the 3D object to the reference camera system. While cycloidal curves are derived as orbits of coupled twist transformations, we apply a spectral domain representation of 3D contours as an extension of cycloidal curves. Their Fourier descriptors are also related to twist representations. A twist is an element of se(3) and is a pair containing two 3D vectors. In a matrix representation, its exponential leads to an element of SE(3) and therefore to a rigid motion. We show that twist representations of objects can numerically efficiently and easily be applied to the freeform pose estimation problem. The pose problem itself is formalized as an implicit problem and we gain constraint equations, which have to be fulfilled with respect to the unknown rigid body motion.
Chapter 1 Monocular Pose Estimation of Kinematic Chains
"... ABSTRACT In this paper conformal geometric algebra is used to formalize an algebraic embedding for the problem of monocular pose estimation of kinematic chains. The problem is modeled on the base of several geometric constraint equations. In conformal geometric algebra the resulting equations are co ..."
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ABSTRACT In this paper conformal geometric algebra is used to formalize an algebraic embedding for the problem of monocular pose estimation of kinematic chains. The problem is modeled on the base of several geometric constraint equations. In conformal geometric algebra the resulting equations are compact and clear. To solve the equations we linearize and iterate the equations to approximate the pose and the kinematic chain parameters. 1.1