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arXiv · 1501.01266

The Quadrifocal Variety

Luke Oeding
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Abstract

Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 8 (and partially in degree 9) using the representations of $\operatorname{GL}(3)^{\times 4}$ in the polynomial ring on the space of $3 \times 3 \times 3 \times 3$ tensors. Further representation-theoretic analysis gives a lower bound for the number of minimal generators.

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Luke Oeding. 2015-01-06. The Quadrifocal Variety. https://doi.org/10.1016/j.laa.2016.09.034

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