# Learn to Scale: Generating Multipolar Normalized Density Maps for Crowd Counting

arXiv: https://arxiv.org/abs/1907.12428 · HTML: https://mlsanity.com/paper/1907.12428/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2019.

## Built on by (most cited first, 30 of 32)

- [An End-to-End Transformer Model for Crowd Localization](https://mlsanity.com/paper/2202.13065/) (2022)
- [TransCrowd: weakly-supervised crowd counting with transformers](https://mlsanity.com/paper/2104.09116/) (2021)
- [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)
- [Focal Inverse Distance Transform Maps for Crowd Localization](https://mlsanity.com/paper/2102.07925/) (2021)
- [Leveraging Self-Supervision for Cross-Domain Crowd Counting](https://mlsanity.com/paper/2103.16291/) (2021)
- [Direct Measure Matching for Crowd Counting](https://mlsanity.com/paper/2107.01558/) (2021)
- [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)
- [Boosting Detection in Crowd Analysis via Underutilized Output Features](https://mlsanity.com/paper/2308.16187/) (2023)
- [Crowd Localization from Gaussian Mixture Scoped Knowledge and Scoped Teacher](https://mlsanity.com/paper/2206.05717/) (2022)
- [DAOT: Domain-Agnostically Aligned Optimal Transport for Domain-Adaptive Crowd Counting](https://mlsanity.com/paper/2308.05311/) (2023)
- [Self-supervised Domain Adaptation in Crowd Counting](https://mlsanity.com/paper/2206.03431/) (2022)
- [Efficient High-Resolution Deep Learning: A Survey](https://mlsanity.com/paper/2207.13050/) (2022)
- [Interactive Class-Agnostic Object Counting](https://mlsanity.com/paper/2309.05277/) (2023)
- [Counting Stacked Objects](https://mlsanity.com/paper/2411.19149/) (2024)
- [Can Current AI Models Count What We Mean, Not What They See? A Benchmark and Systematic Evaluation](https://mlsanity.com/paper/2509.13939/) (2025)
- [VisDrone-CC2020: The Vision Meets Drone Crowd Counting Challenge Results](https://mlsanity.com/paper/2107.08766/) (2021)
- [Glance to Count: Learning to Rank with Anchors for Weakly-supervised Crowd Counting](https://mlsanity.com/paper/2205.14659/) (2022)
- [Towards More Effective PRM-based Crowd Counting via A Multi-resolution Fusion and Attention Network](https://mlsanity.com/paper/2112.09664/) (2021)
- [Shifted Autoencoders for Point Annotation Restoration in Object Counting](https://mlsanity.com/paper/2312.07190/) (2023)
- [Scale-Aware Network with Regional and Semantic Attentions for Crowd Counting under Cluttered Background](https://mlsanity.com/paper/2101.01479/) (2021)
- [Multi-Scale Context Aggregation Network with Attention-Guided for Crowd Counting](https://mlsanity.com/paper/2104.02245/) (2021)
- [Count, Decode and Fetch: A New Approach to Handwritten Chinese Character Error Correction](https://mlsanity.com/paper/2307.16253/) (2023)
- [Consistent-Point: Consistent Pseudo-Points for Semi-Supervised Crowd Counting and Localization](https://mlsanity.com/paper/2503.12441/) (2025)
- [CORDS: Continuous Representations of Discrete Structures](https://mlsanity.com/paper/2601.21583/) (2026)
- [CountEx: Fine-Grained Counting via Exemplars and Exclusion](https://mlsanity.com/paper/2602.19432/) (2026)
- [Automated Counting of Stacked Objects in Industrial Inspection](https://mlsanity.com/paper/2603.15470/) (2026)
- [Enhanced Information Fusion Network for Crowd Counting](https://mlsanity.com/paper/2101.04279/) (2021)
- [An Efficient Additive Kolmogorov-Arnold Transformer for Point-Level Maize Localization in Unmanned Aerial Vehicle Imagery](https://mlsanity.com/paper/2601.07975/) (2026)

## Abstract (arXiv)

Dense crowd counting aims to predict thousands of human instances from an image, by calculating integrals of a density map over image pixels. Existing approaches mainly suffer from the extreme density variances. Such density pattern shift poses challenges even for multi-scale model ensembling. In this paper, we propose a simple yet effective approach to tackle this problem. First, a patch-level density map is extracted by a density estimation model and further grouped into several density levels which are determined over full datasets. Second, each patch density map is automatically normalized by an online center learning strategy with a multipolar center loss. Such a design can significantly condense the density distribution into several clusters, and enable that the density variance can be learned by a single model. Extensive experiments demonstrate the superiority of the proposed method. Our work outperforms the state-of-the-art by 4.2%, 14.3%, 27.1% and 20.1% in MAE, on ShanghaiTech Part A, ShanghaiTech Part B, UCF_CC_50 and UCF-QNRF datasets, respectively.