What is the loss function defined by Mnih and Hinton in their paper “Learning to Label Aerial Images from Noisy Data”?

Question

In section 3.3 of the paper, they state that they use the cross entropy. Then they define the probability for a label to be a false positive as $\theta_0$ and a false negative as $\theta_1$.

They use it to somehow modify the loss function but never actually state what this new loss is.

I was expecting something like

$f_\theta(\hat{m_i}, \tilde{m_i}) = \tilde{m_i} *g_{\theta_0}(\hat{m_i}) + (1-\tilde{m_i})*g_{\theta_1}(1-\hat{m_i})$

but $g$ is not given.