# Direct Measure Matching for Crowd Counting

arXiv: https://arxiv.org/abs/2107.01558 · HTML: https://mlsanity.com/paper/2107.01558/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 4 Jul 2021.

## Builds on (most cited first, 20 of 20)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [CSRNet: Dilated Convolutional Neural Networks for Understanding the Highly Congested Scenes](https://mlsanity.com/paper/1802.10062/) (2018)
- [Composition Loss for Counting, Density Map Estimation and Localization in Dense Crowds](https://mlsanity.com/paper/1808.01050/) (2018)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Bayesian Loss for Crowd Count Estimation with Point Supervision](https://mlsanity.com/paper/1908.03684/) (2019)
- [NWPU-Crowd: A Large-Scale Benchmark for Crowd Counting and Localization](https://mlsanity.com/paper/2001.03360/) (2020)
- [Context-Aware Crowd Counting](https://mlsanity.com/paper/1811.10452/) (2018)
- [Distribution Matching for Crowd Counting](https://mlsanity.com/paper/2009.13077/) (2020)
- [JHU-CROWD++: Large-Scale Crowd Counting Dataset and A Benchmark Method](https://mlsanity.com/paper/2004.03597/) (2020)
- [Point in, Box out: Beyond Counting Persons in Crowds](https://mlsanity.com/paper/1904.01333/) (2019)
- [Generating High-Quality Crowd Density Maps using Contextual Pyramid CNNs](https://mlsanity.com/paper/1708.00953/) (2017)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [Perspective-Guided Convolution Networks for Crowd Counting](https://mlsanity.com/paper/1909.06966/) (2019)
- [DecideNet: Counting Varying Density Crowds Through Attention Guided Detection and Density Estimation](https://mlsanity.com/paper/1712.06679/) (2017)
- [Multi-Level Bottom-Top and Top-Bottom Feature Fusion for Crowd Counting](https://mlsanity.com/paper/1908.10937/) (2019)
- [Learn to Scale: Generating Multipolar Normalized Density Maps for Crowd Counting](https://mlsanity.com/paper/1907.12428/) (2019)
- [Multi-scale Convolutional Neural Networks for Crowd Counting](https://mlsanity.com/paper/1702.02359/) (2017)
- [Crowd counting via scale-adaptive convolutional neural network](https://mlsanity.com/paper/1711.04433/) (2017)

## Built on by (most cited first, 18 of 18)

- [Boosting Crowd Counting via Multifaceted Attention](https://mlsanity.com/paper/2203.02636/) (2022)
- [Rethinking Spatial Invariance of Convolutional Networks for Object Counting](https://mlsanity.com/paper/2206.05253/) (2022)
- [Semi-supervised Crowd Counting via Density Agency](https://mlsanity.com/paper/2209.02955/) (2022)
- [Regressor-Segmenter Mutual Prompt Learning for Crowd Counting](https://mlsanity.com/paper/2312.01711/) (2023)
- [Counting Crowds in Bad Weather](https://mlsanity.com/paper/2306.01209/) (2023)
- [Object Counting: You Only Need to Look at One](https://mlsanity.com/paper/2112.05993/) (2021)
- [Scene-Adaptive Attention Network for Crowd Counting](https://mlsanity.com/paper/2112.15509/) (2021)
- [Multi-modal Crowd Counting via a Broker Modality](https://mlsanity.com/paper/2407.07518/) (2024)
- [CrowdFormer: Weakly-supervised Crowd counting with Improved Generalizability](https://mlsanity.com/paper/2203.03768/) (2022)
- [FGENet: Fine-Grained Extraction Network for Congested Crowd Counting](https://mlsanity.com/paper/2401.01208/) (2024)
- [Semi-supervised Counting via Pixel-by-pixel Density Distribution Modelling](https://mlsanity.com/paper/2402.15297/) (2024)
- [Semi-Supervised Crowd Counting with Contextual Modeling: Facilitating Holistic Understanding of Crowd Scenes](https://mlsanity.com/paper/2310.10352/) (2023)
- [Point-to-Region Loss for Semi-Supervised Point-Based Crowd Counting](https://mlsanity.com/paper/2505.21943/) (2025)
- [Structure-aware Fine-tuning for Code Pre-trained Models](https://mlsanity.com/paper/2404.07471/) (2024)
- [Virtual Classification: Modulating Domain-Specific Knowledge for Multidomain Crowd Counting](https://mlsanity.com/paper/2402.03758/) (2024)
- [2D Gaussians Spatial Transport for Point-supervised Density Regression](https://mlsanity.com/paper/2511.14477/) (2025)
- [Thermal-Only Crowd Counting with Deployment-Time Privacy Protection](https://mlsanity.com/paper/2605.17042/) (2026)
- [A Benchmark for Semi-supervised Multi-modal Crowd Counting](https://mlsanity.com/paper/2606.03646/) (2026)

## Abstract (arXiv)

Traditional crowd counting approaches usually use Gaussian assumption to generate pseudo density ground truth, which suffers from problems like inaccurate estimation of the Gaussian kernel sizes. In this paper, we propose a new measure-based counting approach to regress the predicted density maps to the scattered point-annotated ground truth directly. First, crowd counting is formulated as a measure matching problem. Second, we derive a semi-balanced form of Sinkhorn divergence, based on which a Sinkhorn counting loss is designed for measure matching. Third, we propose a self-supervised mechanism by devising a Sinkhorn scale consistency loss to resist scale changes. Finally, an efficient optimization method is provided to minimize the overall loss function. Extensive experiments on four challenging crowd counting datasets namely ShanghaiTech, UCF-QNRF, JHU++, and NWPU have validated the proposed method.