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.
CITATION STYLE
Triggs, B. (2000). Plane + parallax, tensors and factorization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1842, pp. 522–538). Springer Verlag. https://doi.org/10.1007/3-540-45054-8_34
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