Estimating tensors for matching over multiple views

In this paper we give purely geometric derivations of the constraints between point and line correspondences in multiple views of a static field. The analysis is carried out using geometric algebra, a system which provides a useful tool in many computer vision applications. It is shown that with a s...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 1998-05, Vol.356 (1740), p.1267-1282
Main Authors: Lasenby, Joan, Lasenby, Anthony N.
Format: Article
Language:English
Subjects:
Algebra
Coordinate systems
Degrees of freedom
Dot product of vectors
Geometric Algebra
Geometric planes
Geometry
Grouping and Matching
Linear transformations
Mathematical vectors
Matrices
Minimization
Projective Geometry
Scalars
Tensors
Trifocal Tensor
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Summary:In this paper we give purely geometric derivations of the constraints between point and line correspondences in multiple views of a static field. The analysis is carried out using geometric algebra, a system which provides a useful tool in many computer vision applications. It is shown that with a straightforward geometric interpretation it is simple to derive the degrees of freedom of such tensors and to understand their structure. Given such information, minimal parametrizations of the tensors are possible. Such parametrizations may be useful for estimation of the tensors and subsequent matching of points.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.1998.0221