objectiveness score at position $u$, and $\hat{f_u}$ is 1 if it is identified as being positive for position $u$, and 0 otherwise based on the current label set. For the extra background images, the label is consistently set as 0 and the loss will be always enabled. For the training images in the target domain, we modify it as follows to implement PFOD,

$$\begin{aligned}
l = \begin{cases}
(f_\theta(u) - 1)^2  & \hat{f_u} = 1 \\
f_\theta^2(u) & \hat{f_u} = 0 \text{ \& }  t \le T \\
0 & \hat{f_u} = 0  \text{ \& } t > T
\end{cases}\end{aligned}$$

where $t$ is the number of iterations in SGD, $T$ is a pre-defined parameter (200 in experiments) to determine how many iterations are needed to treat the unknown regions as background. After $T$ iterations, the detector training will only focus on the positive samples and the extra background data.

With the model trained by PFOD, we run the prediction over all the training images from target domain. The predicted bounding boxes with high probability scores (0.9 in experiments) will be merged into the original label set $L^s$ to form $L^{s + 1}$. We also discard any predicted bounding box if it 