the decision boundary. If all the positive and negative samples are known, we can easily figure out the decision boundary to separate true positive and true negative samples, as shown in Fig. \[fig:intuition\](a). When only one positive sample is known and all the rest are unknown, as shown in Fig. \[fig:intuition\](b), if we simply treat all the unknowns as negative sample, the decision boundary could mis-classify the unlabeled positive samples as being negative.

To compensate the lack of negative samples, we can introduce some images as extra negative data, as shown in green from Fig. \[fig:intuition\](c) to Fig. \[fig:intuition\](e). For object detection, it is indeed easy to find images without any target objects in the same domain. For example, we can use the PASCAL VOC [@EveringhamGWWZ10] 2007 data set as extra background images for the problem of car counting on the CARPK [@HsiehLH17] dataset. In Fig. \[fig:intuition\](c) we show how to propagate the labels. We first treat all the unlabeled samples (shown as both blue plus and minus symbols in Fig. \[fig:intuition\](c)) as negative samples to train the detector, and the learned decision boundary will be pushed close to the only positive sample (red plus symbol) as depicted with the 