# From Open Set to Closed Set: Counting Objects by Spatial Divide-and-Conquer

arXiv: https://arxiv.org/abs/1908.06473 · HTML: https://mlsanity.com/paper/1908.06473/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2019.

## Built on by (most cited first, 30 of 48)

- [Rethinking Counting and Localization in Crowds:A Purely Point-Based Framework](https://mlsanity.com/paper/2107.12746/) (2021)
- [Represent, Compare, and Learn: A Similarity-Aware Framework for Class-Agnostic Counting](https://mlsanity.com/paper/2203.08354/) (2022)
- [TransCrowd: weakly-supervised crowd counting with transformers](https://mlsanity.com/paper/2104.09116/) (2021)
- [Rethinking Spatial Invariance of Convolutional Networks for Object Counting](https://mlsanity.com/paper/2206.05253/) (2022)
- [CrowdCLIP: Unsupervised Crowd Counting via Vision-Language Model](https://mlsanity.com/paper/2304.04231/) (2023)
- [STEERER: Resolving Scale Variations for Counting and Localization via Selective Inheritance Learning](https://mlsanity.com/paper/2308.10468/) (2023)
- [Point-Query Quadtree for Crowd Counting, Localization, and More](https://mlsanity.com/paper/2308.13814/) (2023)
- [CCTrans: Simplifying and Improving Crowd Counting with Transformer](https://mlsanity.com/paper/2109.14483/) (2021)
- [Continual Learning with Bayesian Model based on a Fixed Pre-trained Feature Extractor](https://mlsanity.com/paper/2204.13349/) (2022)
- [Leveraging Self-Supervision for Cross-Domain Crowd Counting](https://mlsanity.com/paper/2103.16291/) (2021)
- [Calibrating Uncertainty for Semi-Supervised Crowd Counting](https://mlsanity.com/paper/2308.09887/) (2023)
- [Improving Point-based Crowd Counting and Localization Based on Auxiliary Point Guidance](https://mlsanity.com/paper/2405.10589/) (2024)
- [Uniformity in Heterogeneity:Diving Deep into Count Interval Partition for Crowd Counting](https://mlsanity.com/paper/2107.12619/) (2021)
- [CrowdDiff: Multi-hypothesis Crowd Density Estimation using Diffusion Models](https://mlsanity.com/paper/2303.12790/) (2023)
- [LVLM-COUNT: Enhancing the Counting Ability of Large Vision-Language Models](https://mlsanity.com/paper/2412.00686/) (2024)
- [Discrete-Constrained Regression for Local Counting Models](https://mlsanity.com/paper/2207.09865/) (2022)
- [Redesigning Multi-Scale Neural Network for Crowd Counting](https://mlsanity.com/paper/2208.02894/) (2022)
- [Crowd Counting via Perspective-Guided Fractional-Dilation Convolution](https://mlsanity.com/paper/2107.03665/) (2021)
- [Variational Attention: Propagating Domain-Specific Knowledge for Multi-Domain Learning in Crowd Counting](https://mlsanity.com/paper/2108.08023/) (2021)
- [Boosting Detection in Crowd Analysis via Underutilized Output Features](https://mlsanity.com/paper/2308.16187/) (2023)
- [Scene-Adaptive Attention Network for Crowd Counting](https://mlsanity.com/paper/2112.15509/) (2021)
- [CLIP-EBC: CLIP Can Count Accurately through Enhanced Blockwise Classification](https://mlsanity.com/paper/2403.09281/) (2024)
- [Backdoor Attacks on Crowd Counting](https://mlsanity.com/paper/2207.05641/) (2022)
- [Forget Less, Count Better: A Domain-Incremental Self-Distillation Learning Benchmark for Lifelong Crowd Counting](https://mlsanity.com/paper/2205.03307/) (2022)
- [RGB-D Indiscernible Object Counting in Underwater Scenes](https://mlsanity.com/paper/2304.11677/) (2023)
- [Deep Imbalanced Regression via Hierarchical Classification Adjustment](https://mlsanity.com/paper/2310.17154/) (2023)
- [Every Shot Counts: Using Exemplars for Repetition Counting in Videos](https://mlsanity.com/paper/2403.18074/) (2024)
- [Rethinking Global Context in Crowd Counting](https://mlsanity.com/paper/2105.10926/) (2021)
- [CrowdMLP: Weakly-Supervised Crowd Counting via Multi-Granularity MLP](https://mlsanity.com/paper/2203.08219/) (2022)
- [Semi-supervised Counting via Pixel-by-pixel Density Distribution Modelling](https://mlsanity.com/paper/2402.15297/) (2024)

## Abstract (arXiv)

Visual counting, a task that predicts 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, the collected images and labeled count values are limited in reality, which means only a small closed set is observed. Existing methods typically model this task in a regression manner, while they are likely to suffer from an unseen scene with counts out of the scope of the closed set. In fact, counting is decomposable. A dense region can always be divided until sub-region counts are within the previously observed closed set. Inspired by this idea, we propose a simple but effective approach, Spatial Divide-and- Conquer Network (S-DCNet). S-DCNet only learns from a closed set but can generalize well to open-set scenarios via S-DC. S-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. S-DCNet achieves the state-of-the-art performance on three crowd counting datasets (ShanghaiTech, UCFCC50 and UCF-QNRF), a vehicle counting dataset (TRANCOS) and a plant counting dataset (MTC). Compared to the previous best methods, S-DCNet brings a 20.2% relative improvement on the ShanghaiTech Part B, 20.9% on the UCF-QNRF, 22.5% on the TRANCOS and 15.1% on the MTC. Code has been made available at: https://github. com/xhp-hust-2018-2011/S-DCNet.