Least Square for Grassmann-Cayley Agelbra in Homogeneous Coordinates.
Revised Selected Papers of the GCCV 2013, GPID 2013, PAESNPR 2013, and QACIVA 2013 on Image and Video Technology --- PSIVT 2013 Workshops - Volume 8334(2013)
摘要
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.
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