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, +∞) 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 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). 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 on three crowd counting datasets (ShanghaiTech, UCF_CC_50 and UCF-QNRF), a vehicle counting dataset (TRANCOS) and a plant counting dataset (MTC), with a 7.7% relative improvement on the UCF-QNRF, 33.1% on the TRANCOS, and 26.4% on the MTC. SS-DCNet also reports the state-of-the-art cross-domain performance on crowd counting datasets. Particularly in the task from UCF-QNRF to ShanghaiTech Part_A, SS-DCNet even beats most existing models trained directly on the target domain. Code and models have been made available at: https://tinyurl.com/SS-DCNet.

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Rice density is closely related to yield estimation, growth diagnosis, cultivated area statistics, and management and damage evaluation. Currently, rice density estimation heavily relies on manual sampling and counting, which is inefficient and inaccurate. With the prevalence of digital imagery, computer vision (CV) technology emerges as a promising alternative to automate this task. However, challenges of an in-field environment, such as illumination, scale, and appearance variations, render gaps for deploying CV methods. To fill these gaps towards accurate rice density estimation, we propose a deep learning-based approach called the Scale-Fusion Counting Classification Network (SFC2Net) that integrates several state-of-the-art computer vision ideas. In particular, SFC2Net addresses appearance and illumination changes by employing a multicolumn pretrained network and multilayer feature fusion to enhance feature representation. To ameliorate sample imbalance engendered by scale, SFC2Net follows a recent blockwise classification idea. We validate SFC2Net on a new rice plant counting (RPC) dataset collected from two field sites in China from 2010 to 2013. Experimental results show that SFC2Net achieves highly accurate counting performance on the RPC dataset with a mean absolute error (MAE) of 25.51, a root mean square error (MSE) of 38.06, a relative MAE of 3.82%, and a R2 of 0.98, which exhibits a relative improvement of 48.2% w.r.t. MAE over the conventional counting approach CSRNet. Further, SFC2Net provides high-throughput processing capability, with 16.7 frames per second on 1024×1024 images. Our results suggest that manual rice counting can be safely replaced by SFC2Net at early growth stages. Code and models are available online at https://git.io/sfc2net.