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

Haipeng Xiong, Hao Lu, Chengxin Liu, Liang Liu, Chunhua Shen, Zhiguo Cao
2020 arXiv   pre-print
Visual counting, a task that aims to estimate the number of objects from an image/video, is an open-set problem by nature, i.e., the number of population can vary in [0, inf) in theory. However, collected data and labeled instances are limited in reality, which means that only a small closed set is observed. Existing methods typically model this task in a regression manner, while they are prone to suffer from an unseen scene with counts out of the scope of the closed set. In fact, counting has
more » ... n 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). Thus, SS-DCNet can only learn from a closed set but generalize well to open-set scenarios via S-DC. SS-DCNet is also efficient. To avoid repeatedly computing sub-region convolutional features, S-DC is executed on the feature map instead of on the input image. We provide theoretical analyses as well as a controlled experiment on toy data, demonstrating why closed-set modeling makes sense. Extensive experiments show that SS-DCNet achieves the state-of-the-art performance. Code and models are available at: https://tinyurl.com/SS-DCNet.
arXiv:2001.01886v2 fatcat:wskpcl2wdjdh7bmlge45ymoalm