The cubic growth conjecture for the Euclidean distance degree of affine multiview varieties

Let $A_1,A_2,\ldots,A_n$ be general projective cameras, and let $X_n\subseteq\mathbb{R}^{2n}$ be the affine multiview variety obtained by dehomogenizing the multiview variety associated to these cameras. The Euclidean distance degree, denoted by ${\rm EDdegree}(X_n)$, is the number of complex critical points of the squared Euclidean distance function from a general data point to $X_n$. The cubic growth conjecture. The Euclidean distance degree of the affine multiview variety $X_n$ equals

$${\rm EDdegree}(X_n) \quad = \quad \frac{9}{2} n^3 - \frac{21}{2} n^2 + 8 n - 4.$$

The conjecture is suggested by the computed values for $n=2,\ldots,7$, and predicts that these Euclidean distance degrees grow as a cubic polynomial in the number of cameras.