# Progressive Multi-resolution Loss for Crowd Counting

arXiv: https://arxiv.org/abs/2212.04127 · HTML: https://mlsanity.com/paper/2212.04127/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 58 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [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)
- [Bayesian Loss for Crowd Count Estimation with Point Supervision](https://mlsanity.com/paper/1908.03684/) (2019)
- [Rethinking Counting and Localization in Crowds:A Purely Point-Based Framework](https://mlsanity.com/paper/2107.12746/) (2021)
- [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)
- [Learning from Synthetic Data for Crowd Counting in the Wild](https://mlsanity.com/paper/1903.03303/) (2019)
- [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)
- [Switching Convolutional Neural Network for Crowd Counting](https://mlsanity.com/paper/1708.00199/) (2017)
- [An End-to-End Transformer Model for Crowd Localization](https://mlsanity.com/paper/2202.13065/) (2022)
- [Locate, Size and Count: Accurately Resolving People in Dense Crowds via Detection](https://mlsanity.com/paper/1906.07538/) (2019)
- [Leveraging Unlabeled Data for Crowd Counting by Learning to Rank](https://mlsanity.com/paper/1803.03095/) (2018)
- [Rethinking Spatial Invariance of Convolutional Networks for Object Counting](https://mlsanity.com/paper/2206.05253/) (2022)
- [From Open Set to Closed Set: Counting Objects by Spatial Divide-and-Conquer](https://mlsanity.com/paper/1908.06473/) (2019)
- [Crowd Counting with Deep Structured Scale Integration Network](https://mlsanity.com/paper/1908.08692/) (2019)
- [Multi-Level Bottom-Top and Top-Bottom Feature Fusion for Crowd Counting](https://mlsanity.com/paper/1908.10937/) (2019)
- [Focal Inverse Distance Transform Maps for Crowd Localization](https://mlsanity.com/paper/2102.07925/) (2021)
- [AutoScale: Learning to Scale for Crowd Counting and Localization](https://mlsanity.com/paper/1912.09632/) (2019)
- [SCAR: Spatial-/Channel-wise Attention Regression Networks for Crowd Counting](https://mlsanity.com/paper/1908.03716/) (2019)
- [Adaptive Mixture Regression Network with Local Counting Map for Crowd Counting](https://mlsanity.com/paper/2005.05776/) (2020)
- [Semi-supervised Crowd Counting via Density Agency](https://mlsanity.com/paper/2209.02955/) (2022)
- [Redesigning Multi-Scale Neural Network for Crowd Counting](https://mlsanity.com/paper/2208.02894/) (2022)

## Built on by (most cited first, 4 of 4)

- [Semi-Supervised Crowd Counting with Contextual Modeling: Facilitating Holistic Understanding of Crowd Scenes](https://mlsanity.com/paper/2310.10352/) (2023)
- [The Effectiveness of a Simplified Model Structure for Crowd Counting](https://mlsanity.com/paper/2404.07847/) (2024)
- [Depth-Assisted Network for Indiscernible Marine Object Counting with Adaptive Motion-Differentiated Feature Encoding](https://mlsanity.com/paper/2503.08152/) (2025)
- [Remote Sensing Object Counting with Online Knowledge Learning](https://mlsanity.com/paper/2303.10318/) (2023)

## Abstract (arXiv)

Crowd counting is usually handled in a density map regression fashion, which is supervised via a L2 loss between the predicted density map and ground truth. To effectively regulate models, various improved L2 loss functions have been proposed to find a better correspondence between predicted density and annotation positions. In this paper, we propose to predict the density map at one resolution but measure the density map at multiple resolutions. By maximizing the posterior probability in such a setting, we obtain a log-formed multi-resolution L2-difference loss, where the traditional single-resolution L2 loss is its particular case. We mathematically prove it is superior to a single-resolution L2 loss. Without bells and whistles, the proposed loss substantially improves several baselines and performs favorably compared to state-of-the-art methods on four crowd counting datasets, ShanghaiTech A & B, UCF-QNRF, and JHU-Crowd++.