resort to a problem setting where each image is only partially annotated with a few bounding boxes and leaves other instances unlabeled. This setting is practically useful especially when the number of instances is large and it is tedious and costly to label all the instances. Another motivation is that in certain object counting problem, the large number of instances exhibits less variances, e.g. scale, color. Potentially, a few annotated bounding boxes might generalize well to achieve a high accuracy. We call the learning algorithm trained on such training data *incompletely-supervised learning*. Fig. \[fig:isl\] shows examples to illustrate the training image difference among the fully-supervised, weakly-supervised, and incompletely-supervised learning. For the fully-supervised setting, all cars and drinks are annotated. The total number of the car instances is as many as 58. In the weakly-supervised setting, we only have the information that the car or drinks exist in the image. Based on the observation that in many object counting problems the target objects are normally repeated and highly similar to each other, we are particularly interested in the setting when only a few exemplar annotations are provided, which is illustrated in Fig. \[fig:isl\](c)

In incompletely-supervised learning, if any unlabeled region is 