On the geometry and algebra of the point and line correspondences between N images
Top Cited Papers
- 19 November 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 951-956
- https://doi.org/10.1109/iccv.1995.466832
Abstract
We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the Grassmann-Cayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effective way (i.e. allowing actual computation if needed). We have a fairly complete picture of the situation in the case of points; there are only three types of algebraic relations which are satisfied by the coordinates of the images of a 3-D point: bilinear relations arising when we consider pairs of images among the N and which are the well-known epipolar constraints, trilinear relations arising when we consider triples of images among the N, and quadrilinear relations arising when we consider four-tuples of images among the N. In the case of lines, we show how the traditional perspective projection equation can be suitably generalized and that in the case of three images there exist two independent trilinear relations between the coordinates of the images of a 3-D line.<>Keywords
This publication has 3 references indexed in Scilit:
- On the geometry and algebra of the point and line correspondences between N imagesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Algebraic functions for recognitionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1995
- Algorithms in Invariant TheoryPublished by Springer Nature ,1993