The multiview conjecture for the Euclidean distance degree

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Let XmX_m be the affine multiview variety of m≥3m\geq 3 cameras in general position, and let EDdeg⁡(Xm)\operatorname{EDdeg}(X_m) denote its Euclidean distance degree. Multiview conjecture. The Euclidean distance degree is

EDdeg⁡(Xm)=92m3−212m2+8m−4.\operatorname{EDdeg}(X_m)=\frac{9}{2}m^3-\frac{21}{2}m^2+8m-4.

This explicit formula was proposed from numerical computations for configurations involving m≤7m\leq 7 cameras. Its validity for general mm is not established in the supplied text.

References

Primary source

Laurentiu Maxim, Jose Israel Rodriguez and Botong Wang, “Applications of singularity theory in applied algebraic geometry and algebraic statistics”, arXiv:2305.19842 (2023).

Additional references

2 papers in this index state this conjecture (2018–2023). The statement above is taken from the most recent of them; the others are arXiv:1812.05648.

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