names are shown in bottom left []{data-label="fig:isl"}](figs/CARPK_isl_4.jpg "fig:"){width="\thirdsplitwidth\linewidth"}
   ![Different training image settings in detection-based object counting. The label names are shown in bottom left []{data-label="fig:isl"}](figs/CocoBottle1024DrinkY_fsl.jpg "fig:"){width="\thirdsplitwidth\linewidth"}   ![Different training image settings in detection-based object counting. The label names are shown in bottom left []{data-label="fig:isl"}](figs/CocoBottle1024DrinkY_wsl.jpg "fig:"){width="\thirdsplitwidth\linewidth"}   ![Different training image settings in detection-based object counting. The label names are shown in bottom left []{data-label="fig:isl"}](figs/CocoBottle1024DrinkY_isl_9.jpg "fig:"){width="\thirdsplitwidth\linewidth"}
                                                                                                    \(a) Fully-Supervised                                                                                                                                                                                                      \(b) Weakly-Supervised                                                                                                                                                                                                   \(c) Incompletely-Supervised
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In recent years, the accuracy of object detection has been dramatically improved [@Girshick15; @RenHGS15; @LiuAESRFB16; @RedmonF17] thanks to the advance of deep convolutional neural network. However, the high accuracy is achieved normally with the large number of fully annotated bounding boxes. In the context of object counting, the number of instances even in a single image could be huge (e.g. from tens to hundreds), which not only presents a great challenge to object detection, but also requires tremendous annotation effort to build a high-accuracy object detector.

To save the annotation cost, weakly supervised approaches are generally adopted to train the model solely based on image-level annotations. However, such approaches still suffer from suboptimal accuracy due to the lack of instance-level (e.g. bounding box) annotations. To address this problem, we 