Three-dimensional object recognition from single two-dimensional images
Artificial Intelligence
Object recognition by computer: the role of geometric constraints
Object recognition by computer: the role of geometric constraints
Pose Determination from Line-to-Plane Correspondences: Existence Condition and Closed-Form Solutions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating 3-D location parameters using dual number quaternions
CVGIP: Image Understanding
Pose Estimation by Fusing Noisy Data of Different Dimensions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Object pose from 2-D to 3-D point and line correspondences
International Journal of Computer Vision
Estimating 3-D rigid body transformations: a comparison of four major algorithms
Machine Vision and Applications - Special issue on performance evaluation
Geometric methods and applications: for computer science and engineering
Geometric methods and applications: for computer science and engineering
Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics
New algebraic tools for classical geometry
Geometric computing with Clifford algebras
Generalized homogeneous coordinates for computational geometry
Geometric computing with Clifford algebras
Honing geometric algebra for its use in the computer sciences
Geometric computing with Clifford algebras
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
The Multidimensional Isotropic Generalization of Quadrature Filters in Geometric Algebra
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
Hierarchical Recognition of Articulated Objects from Single Perspective Views
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Tracking People with Twists and Exponential Maps
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Analysis of Orientation Problems Using Plucker Lines
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
Pose Estimation in Conformal Geometric Algebra Part I: The Stratification of Mathematical Spaces
Journal of Mathematical Imaging and Vision
Pose Estimation in Conformal Geometric Algebra Part I: The Stratification of Mathematical Spaces
Journal of Mathematical Imaging and Vision
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra: A Powerful Tool for Solving Geometric Problems in Visual Computing
SIBGRAPI-TUTORIALS '09 Proceedings of the 2009 Tutorials of the XXII Brazilian Symposium on Computer Graphics and Image Processing
Stochastically optimal epipole estimation in omnidirectional images with geometric algebra
RobVis'08 Proceedings of the 2nd international conference on Robot vision
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Projective model for central catadioptric cameras using clifford algebra
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Target calibration and tracking using conformal geometric algebra
PSIVT'06 Proceedings of the First Pacific Rim conference on Advances in Image and Video Technology
Linear pose estimate from corresponding conics
Pattern Recognition
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Part II uses the foundations of Part I [35] to define constraint equations for 2D-3D pose estimation of different corresponding entities. Most articles on pose estimation concentrate on specific types of correspondences, mostly between points, and only rarely use line correspondences. The first aim of this part is to extend pose estimation scenarios to correspondences of an extended set of geometric entities. In this context we are interested to relate the following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point, 2D line/3D line, 2D conic/3D circle, 2D conic/3D sphere. Furthermore, to handle articulated objects, we describe kinematic chains in this context in a similar manner. We ensure that all constraint equations end up in a distance measure in the Euclidean space, which is well posed in the context of noisy data. We also discuss the numerical estimation of the pose. We propose to use linearized twist transformations which result in well conditioned and fast solvable systems of equations. The key idea is not to search for the representation of the Lie group, describing the rigid body motion, but for the representation of their generating Lie algebra. This leads to real-time capable algorithms.