a positiveness-focused object detector (PFOD) []{data-label="fig:framework"}](figs/framework.pdf){width="0.99\linewidth"}

### Solution.

Fig. \[fig:framework\] shows the framework of the proposed strategy to learn the object detector. At the initial state of training, the bounding boxes we have are the labeled set, i.e. $L^1 = \{\mathbf{x}_i | i= 1, \ldots, M_1\}$ for each training image. Based on $L^s$, we train a positiveness-focused object detector (PFOD), which can be based on any object detector [@GirshickDDM14; @Girshick15; @RenHGS15; @LiuAESRFB16; @RedmonF17]. In this work, we choose YoloV2 [@RedmonF17] for its simplicity. The network first processes each training image in a batch manner by a fully convolutional neural network, and then outputs three components at each spatial position: bounding box coordinates, objectiveness to tell how confident the bounding box contains an object, and classification scores to tell which category the bounding box contains. Here we assume the number of categories is 1 and remove the classification module. The Euclidean loss is used for bounding box coordinate regression and objectiveness confidence regression. Specifically, for the objectiveness at spatial position $u$, the loss is defined as $$\begin{aligned}
    l = (f_\theta(u) - \hat{f_u})^2\end{aligned}$$ where $\theta$ is the network parameter, learned iteratively through the mini-batch stochastic gradient descent (SGD) algorithm, $f_\theta(u)$ is the 