Tensor Algebra: A Combinatorial Approach to the Projective Geometry of Figures

This paper explores the combinatorial aspects of symmetric and anti-symmetric forms represented in tensor algebra. The development of geometric perspective gained from tensor algebra has resulted in the discovery of a novel projection operator for the Chow form of a curve in ℙ3 with applications to computer vision.

[1]  Gian-Carlo Rota,et al.  Invariant theory and superalgebras , 1987 .

[2]  B. Sagan.  The Symmetric Group , 2001 .

[3]  Neil L. White,et al.  Geometric applications of the grassmann-cayley algebra , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[4]  E. Keith Lloyd.  INVARIANT THEORY AND SUPERALGEBRAS (CBMS Regional Conference Series in Mathematics 69) , 1989 .

[5]  Bernd Sturmfels,et al.  Algorithms in invariant theory , 1993, Texts and monographs in symbolic computation.

[6]  Bruce E. Sagan,et al.  The symmetric group - representations, combinatorial algorithms, and symmetric functions , 2001, Wadsworth & Brooks / Cole mathematics series.

[7]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[8]  Amnon Shashua,et al.  Multiple view geometry of non-planar algebraic curves , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[9]  Brian C. Lovell,et al.  Towards Closed Form Solutions to the MultiView Constraints of Curves and Surfaces , 2003, DICTA.

[10]  D. Pedoe.  On a new analytical representation of curves in space , 1947, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[12]  Joe W. Harris,et al.  Algebraic Geometry: A First Course , 1995 .

[13]  B. Triggs.  The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image , 1995 .

[14]  B. L. Waerden,et al.  Zur algebraischen Geometrie. IX , 1937 .

[15]  Bill Triggs,et al.  Matching constraints and the joint image , 1995, Proceedings of IEEE International Conference on Computer Vision.

[16]  Anders Heyden,et al.  Using conic correspondences in two images to estimate the epipolar geometry , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[17]  Olivier D. Faugeras,et al.  On the geometry and algebra of the point and line correspondences between N images , 1995, Proceedings of IEEE International Conference on Computer Vision.

[18]  Andrew Zisserman,et al.  Multiple view geometry in computer visiond , 2001 .

[19]  I. M. Gelʹfand,et al.  Discriminants, Resultants, and Multidimensional Determinants , 1994 .