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
Object pose from 2-D to 3-D point and line correspondences
International Journal of Computer Vision
A fully projective formulation to improve the accuracy of Lowe's pose-estimation algorithm
Computer Vision and Image Understanding
Geometric methods and applications: for computer science and engineering
Geometric methods and applications: for computer science and engineering
Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration
Journal of Mathematical Imaging and Vision
Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics
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
Pose Estimation in the Language of Kinematics
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
A Passive Real-Time Gaze Estimation System for Human-Machine Interfaces
CAIP '97 Proceedings of the 7th International Conference on Computer Analysis of Images and Patterns
Adaptive Pose Estimation for Different Corresponding Entities
Proceedings of the 24th DAGM Symposium on Pattern Recognition
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
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
3D Motion from structures of points, lines and planes
Image and Vision Computing
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Stochastically optimal epipole estimation in omnidirectional images with geometric algebra
RobVis'08 Proceedings of the 2nd international conference on Robot vision
Pose estimation from uncertain omnidirectional image data using line-plane correspondences
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Kernel particle filter for visual quality inspection from monocular intensity images
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Geometry and kinematics with uncertain data
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Estimation of geometric entities and operators from uncertain data
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
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2D-3D 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 2D-3D 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 (e.g. 3D projection rays or 3D reconstructed planes) and express constraints in the 3D space. It turns out that the stratification hierarchy [11] introduced by Faugeras is involved in the scenario. But since the stratification hierarchy is based on pure point concepts a new algebraic embedding is required when dealing with higher order entities. The conformal geometric algebra (CGA) [24] is well suited to solve this problem, since it subsumes the involved mathematical spaces. Operators are defined to switch entities between the algebras of the conformal space and its Euclidean and projective subspaces. This leads to another interpretation of the stratification hierarchy, which is not restricted to be based solely on point concepts. This work summarizes the theoretical foundations needed to deal with the pose problem. Therefore it contains mainly basics of Euclidean, projective and conformal geometry. Since especially conformal geometry is not well known in computer science, we recapitulate the mathematical concepts in some detail. We believe that this geometric model is useful also for many other computer vision tasks and has been ignored so far. Applications of these foundations are presented in Part II [36].