Conformal geometric algebra for robotic vision

Journal of Mathematical Imaging and Vision

Volumn 24, Issue 1, 2006, Pages 55-81

  Bayro Corrochano, Eduardo ^a   Reyes Lozano, Leo ^b   Zamora Esquivel, Julio ^b  

^a UNIDAD GUADALAJARA   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

3D range data; 3D rigid motion; Clifford (geometric) algebra; Computer vision; Directed distance; Incidence algebra; Laser and stereo system; Projective and affine geometry; Spheres projective geometry; Visually guided robotics

Indexed keywords

3D RANGE DATA; 3D RIGID MOTION; CLIFFORD (GEOMETRIC) ALGEBRA; DIRECTED DISTANCE; INCIDENCE ALGEBRA; LASER AND STEREO SYSTEM; PROJECTIVE AND AFFINE GEOMETRY; SPHERES PROJECTIVE GEOMETRY; VISUALLY GUIDED ROBOTICS;

ALGEBRA; COMPUTATION THEORY; GEOMETRY; KINEMATICS; MATHEMATICAL TRANSFORMATIONS; ROBOTS;

COMPUTER VISION;

EID: 33144481517     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-005-3615-1     Document Type: Article

References (13)

1. E. Bayro-Corrochano, Geometric Computing for Perception Action Systems, Springer Verlag: Boston, 2001.
2. E. Bayro-Corrochano, K. Daniilidis, and G. Sommer, "Motor algebra for 3D kinematics. The case of the hand-eye calibration," Journal of Mathematical Imaging and Vision, Vol. 13, pp. 79-99, 2000.
3. E. Bayro-Corrochano and J. Lasenby, "Object modelling and motion analysis using Clifford algebra," in Proceedings of Europe-China Workshop on Geometric Modeling and Invariants for Computer Vision, Roger Mohr and Wu Chengke (Eds.), Xi'an, China, April 27-29, 1995. pp. 143-149,
4. E. Bayro-Corrochano, J. Lasenby, and G. Sommer, Geometric algebra: A framework for computing point and line correspondences and projective structure using n-uncalibrated cameras," in Proceedings of the International Conference on Pattern Recognition (ICPR'96), Vienna, August 1996, Vol. I, pp. 393-397.
5. G. Csurka and O. Faugeras, "Computing three dimensional project invariants from a pair of images using the Grassmann-Cayley algebra," Journal of Image and Vision Computing,
6. D. Hestenes, Space-Time Algebra, Gordon and Breach, 1966.
7. D. Hestenes, "Old wine in new botles: A new algebraic framework for computational geometry," in Advances in Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkhauser: Boston, Chap. 1, pp. 1-25, 2001.
8. D. Hestenes, H. Li, and A. Rockwood, "New algebraic tools for classical geometry," in Geometric Computing with Clifford Algebra, G. Sommer (Ed.). Springer-Verlag: Berlin Heidelberg, Chap.I, pp. 3-23, 2001.
9. D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics," D. Reidel: Dordrecht, 1984.
10. D. Hestenes, and R. Ziegler, "Projective geometry with Clifford algebra," Acta Applicandae Mathematicae, Vol. 23, pp. 25-63, 1991.
11. J. Laseby and E. Bayro-Corrochano, "Analysis and computation of projective invariants from multiple views in the geometric algebra framework," in Special Issue on Invariants for Pattern Recognition and Classification, M. A. Rodrigues (Ed.). Int. Journal of Pattern Recognition and Artificial Intelligence, Vol. 13, No. 8, pp. 1105-1121, 1999.
12. J. Lasenby, A.N. Lasenby, C.J.L. Doran, and W.J. Fitzgerald, "New geometric methods for computer vision - an application to structure and motion estimation," International Journal of Computer Vision, Vol. 26, No. 3, pp. 191-213, 1998.
13. N. White, "Geometric applications of the Grassman-Cayley algebra," in Handbook of Discrete and Computational Geometry, J.E. Goodman and J. O'Rourke (Eds.), CRC Press: Florida, 1997.