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Plane + Parallax, Tensors and Factorization

Bill Triggs 1 
1 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : We study the special form that the general multi-image tensor formalism takes under the plane + parallax decomposition, including matching tensors and constraints, closure and depth recovery relations, and inter-tensor consistency constraints. Plane + parallax alignment greatly simplifies the algebra, and uncovers the underlying geometric content. We relate plane + parallax to the geometry of translating, calibrated cameras, and introduce a new parallax-factorizing projective reconstruction method based on this. Initial plane + parallax alignment reduces the problem to a single rank-one factorization of a matrix of rescaled parallaxes into a vector of projection centres and a vector of projective heights above the reference plane. The method extends to 3D lines represented by via-points and 3D planes represented by homographies.
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Bill Triggs. Plane + Parallax, Tensors and Factorization. 6th European Conference on Computer Vision (ECCV '00), Jun 2000, Dublin, Ireland. pp.522--538, ⟨10.1007/3-540-45054-8_34⟩. ⟨inria-00548289⟩



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