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Least Square for Grassmann-Cayley Agelbra in Homogeneous Coordinates

Abstract : 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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https://hal-upec-upem.archives-ouvertes.fr/hal-01510077
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Submitted on : Wednesday, April 19, 2017 - 4:56:32 AM
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Vincent Lesueur, Vincent Nozick. Least Square for Grassmann-Cayley Agelbra in Homogeneous Coordinates. GCCV 2013, Oct 2013, Guanajuato, Mexico. pp.133 - 144, ⟨10.1007/978-3-642-53926-8_13⟩. ⟨hal-01510077⟩

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