# Semi-supervised Counting via Pixel-by-pixel Density Distribution Modelling

arXiv: https://arxiv.org/abs/2402.15297 · HTML: https://mlsanity.com/paper/2402.15297/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 69 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers](https://mlsanity.com/paper/2012.15840/) (2020)
- [Per-Pixel Classification is Not All You Need for Semantic Segmentation](https://mlsanity.com/paper/2107.06278/) (2021)
- [Segmenter: Transformer for Semantic Segmentation](https://mlsanity.com/paper/2105.05633/) (2021)
- [End-to-End Video Instance Segmentation with Transformers](https://mlsanity.com/paper/2011.14503/) (2020)
- [Transformer Tracking](https://mlsanity.com/paper/2103.15436/) (2021)
- [TransTrack: Multiple Object Tracking with Transformer](https://mlsanity.com/paper/2012.15460/) (2020)
- [CrowdHuman: A Benchmark for Detecting Human in a Crowd](https://mlsanity.com/paper/1805.00123/) (2018)
- [CSRNet: Dilated Convolutional Neural Networks for Understanding the Highly Congested Scenes](https://mlsanity.com/paper/1802.10062/) (2018)
- [Transformer Meets Tracker: Exploiting Temporal Context for Robust Visual Tracking](https://mlsanity.com/paper/2103.11681/) (2021)
- [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 Transformer-based Set Prediction for Object Detection](https://mlsanity.com/paper/2011.10881/) (2020)
- [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)
- [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)
- [End-to-End Object Detection with Adaptive Clustering Transformer](https://mlsanity.com/paper/2011.09315/) (2020)
- [Dual Student: Breaking the Limits of the Teacher in Semi-supervised Learning](https://mlsanity.com/paper/1909.01804/) (2019)
- [Switching Convolutional Neural Network for Crowd Counting](https://mlsanity.com/paper/1708.00199/) (2017)
- [Boosting Crowd Counting via Multifaceted Attention](https://mlsanity.com/paper/2203.02636/) (2022)
- [Point in, Box out: Beyond Counting Persons in Crowds](https://mlsanity.com/paper/1904.01333/) (2019)
- [TransCrowd: weakly-supervised crowd counting with transformers](https://mlsanity.com/paper/2104.09116/) (2021)
- [Leveraging Unlabeled Data for Crowd Counting by Learning to Rank](https://mlsanity.com/paper/1803.03095/) (2018)
- [Perspective-Guided Convolution Networks for Crowd Counting](https://mlsanity.com/paper/1909.06966/) (2019)

## Built on by (most cited first, 7 of 7)

- [Point-to-Region Loss for Semi-Supervised Point-Based Crowd Counting](https://mlsanity.com/paper/2505.21943/) (2025)
- [Consistent-Point: Consistent Pseudo-Points for Semi-Supervised Crowd Counting and Localization](https://mlsanity.com/paper/2503.12441/) (2025)
- [TCFormer: A 5M-Parameter Transformer with Density-Guided Aggregation for Weakly-Supervised Crowd Counting](https://mlsanity.com/paper/2512.22203/) (2025)
- [Getting the Numbers Rightunicodex2014Modelling Multi-Class Object Counting in Dense and Varied Scenes](https://mlsanity.com/paper/2510.02213/) (2025)
- [Exclusivity-Guided Mask Learning for Semi-Supervised Crowd Instance Segmentation and Counting](https://mlsanity.com/paper/2603.16241/) (2026)
- [Granular Ball Guided Stable Latent Domain Discovery for Domain-General Crowd Counting](https://mlsanity.com/paper/2603.24106/) (2026)
- [A Benchmark for Semi-supervised Multi-modal Crowd Counting](https://mlsanity.com/paper/2606.03646/) (2026)

## Abstract (arXiv)

This paper focuses on semi-supervised crowd counting, where only a small portion of the training data are labeled. We formulate the pixel-wise density value to regress as a probability distribution, instead of a single deterministic value. On this basis, we propose a semi-supervised crowd-counting model. Firstly, we design a pixel-wise distribution matching loss to measure the differences in the pixel-wise density distributions between the prediction and the ground truth; Secondly, we enhance the transformer decoder by using density tokens to specialize the forwards of decoders w.r.t. different density intervals; Thirdly, we design the interleaving consistency self-supervised learning mechanism to learn from unlabeled data efficiently. Extensive experiments on four datasets are performed to show that our method clearly outperforms the competitors by a large margin under various labeled ratio settings. Code will be released at https://github.com/LoraLinH/Semi-supervised-Counting-via-Pixel-by-pixel-Density-Distribution-Modelling.