The Chern-Mather class of the multiview variety

Corey Harris; Daniel Lowengrub

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arXiv · 1701.07079

The Chern-Mather class of the multiview variety

Corey Harris·Daniel Lowengrub

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Abstract

The multiview variety associated to a collection of $N$ cameras records which sequences of image points in $\mathbb{P}^{2N}$ can be obtained by taking pictures of a given world point $x\in\mathbb{P}^3$ with the cameras. In order to reconstruct a scene from its picture under the different cameras it is important to be able to find the critical points of the function which measures the distance between a general point $u\in\mathbb{P}^{2N}$ and the multiview variety. In this paper we calculate a specific degree $3$ polynomial that computes the number of critical points as a function of $N$. In order to do this, we construct a resolution of the multiview variety, and use it to compute its Chern-Mather class.

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BibTeX RIS

Corey Harris, Daniel Lowengrub. 2017-01-24. The Chern-Mather class of the multiview variety. https://arxiv.org/abs/1701.07079

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