From Open Set to Closed Set: Supervised Spatial Divide-and-Conquer for Object Counting

Visual counting, a task that aims to estimate the number of objects from an image/video, is an open-set problem by nature as the number of population can vary in \([0,+\infty )\) in theory. However, collected data are limited in reality, which means that only a closed set is observed. Existing methods typically model this task through regression, while they are prone to suffer from unseen scenes with counts out of the scope of the closed set. In fact, counting has an interesting and exclusive property—spatially decomposable. A dense region can always be divided until sub-region counts are within the previously observed closed set. We therefore introduce the idea of spatial divide-and-conquer (S-DC) that transforms open-set counting into a closed set problem. This idea is implemented by a novel Supervised Spatial Divide-and-Conquer Network (SS-DCNet). It can learn from a closed set but generalize to open-set scenarios via S-DC. We provide mathematical analyses and a controlled experiment on synthetic data, demonstrating why closed-set modeling works well. Experiments show that SS-DCNet achieves state-of-the-art performance in crowd counting, vehicle counting and plant counting. SS-DCNet also demonstrates superior transferablity under the cross-dataset setting. Code and models are available at: https://​git.​io/​SS-DCNet.