Least Square for Grassmann-Cayley Agelbra in Homogeneous Coordinates

  • Vincent Lesueur
  • Vincent Nozick
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8334)


This paper presents some tools for least square computation in Grassmann-Cayley algebra, more specifically for elements expressed in homogeneous coordinates. We show that building objects with the outer product from k-vectors of same grade presents some properties that can be expressed in term of linear algebra and can be treated as a least square problem. This paper mainly focuses on line and plane fitting and intersections computation, largely used in computer vision. We show that these least square problems written in Grassmann-Cayley algebra have a direct reformulation in linear algebra, corresponding to their standard expression in projective geometry and hence can be solved using standard least square tools.


Grassmann-Cayley algebra least square line fitting plane fitting intersection 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Vincent Lesueur
    • 1
  • Vincent Nozick
    • 1
  1. 1.Gaspard Monge Institute, UMR 8049Université Paris-Est Marne-la-ValléeFrance

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