Computing 3D projective invariants from points and lines
In this paper we will look at some 3D projective invariants for both point and line matches over several views and, in the case of points, give explicit expressions for forming these invariants in terms of the image coordinates. We discuss whether such invariants are useful by looking at their formation on simulated data.
KeywordsProjective Geometry Fundamental Matrix Geometric Algebra Geometric Product World Point
Unable to display preview. Download preview PDF.
- 1.Bayro-Corrochano, E., Lasenby, J. and Sommer, G. 1996. Geometric Algebra: a framework for computing point and line correspondences and projective structure using n-uncalibrated cameras. Proceedings of the International Conference on Pattern Recognition (ICPR'96), Vienna, August 1996.Google Scholar
- 2.Carlsson, S. 1994. The Double Algebra: and effective tool for computing invariants in computer vision. Applications of Invariance in Computer Vision. Lecture Notes in Computer Science 825; Proceedings of 2nd-joint Europe-US workshop, Azores, October 1993. Eds. Mundy, Zisserman and Forsyth. Springer-Verlag.Google Scholar
- 3.Clifford, W.K. 1878. Applications of Grassmann's extensive algebra. am. J. Math. 1: 350–358.Google Scholar
- 4.Csurka, G. and Faugeras. O. 1995. Computing three-dimensional projective invariants from a pair of images using the Grassmann-Cayley algebra. Proceedings of Europe-China Workshop on Geometric Modeling and Invariants for Computer Vision, Ed. Roger Mohr and Wu Chengke, Xi'an China, April 1995.Google Scholar
- 6.Hestenes, D. 1986. New Foundations for Classical Mechanics D. Reidel, Dordrecht.Google Scholar
- 7.Hestenes, D. and Sobczyk, G. 1984. Clifford Algebra to Geometric Calculus: A unified language for mathematics and physics. D. Reidel, Dordrecht.Google Scholar
- 9.Lasenby, J., Bayro-Corrochano. E., Lasenby, A. and Sommer, G. 1996. A new methodology for computing invariants in computer vision. Proceedings of the International Conference on Pattern Recognition (ICPR'96), Vienna, August 1996.Google Scholar
- 10.Lasenby, J., Bayro-Corrochano, E., Lasenby, A. and Sommer, G. 1996. A New Framework for the Computation of Invariants and Multiple-View Constraints in Computer Vision. Proceedings of the International Conference on Image Processing (ICIP). Lausanne, September 1996.Google Scholar
- 11.Lasenby, J., Bayro-Corrochano, E., Lasenby, A. and Sommer, G. 1996. A New Methodology for the Computation of Invariants in Computer Vision. Cambridge University Engineering Department Technical Report, CUED /F-INENG/TR.244.Google Scholar