#weighted-loss

U-Net weights its pixel-wise cross-entropy with $w(x) = w_c(x) + w_0 \exp\left(-\frac{(d_1(x) + d_2(x))^2}{2\sigma^2}\right)$, where $d_1$ and $d_2$ are the distances to the borders of the nearest and the second nearest cell, $w_0 = 10$ and $\sigma = 5$ pixels. A background pixel between two touching cells has $w_c(x) = 1$, $d_1 = 2$ and $d_2 = 4$. What is $w(x)$?