The multiview conjecture for the Euclidean distance degree

Let XmX_m be the affine multiview variety of m3m\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)=92m3212m2+8m4.\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 m7m\leq 7 cameras. Its validity for general mm is not established in the supplied text.

Sources & referencesView supporting material

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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