# Localization in the Crowd with Topological Constraints

arXiv: https://arxiv.org/abs/2012.12482 · HTML: https://mlsanity.com/paper/2012.12482/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 30 of 68)

- [Rethinking Counting and Localization in Crowds:A Purely Point-Based Framework](https://mlsanity.com/paper/2107.12746/) (2021)
- [Learning To Count Everything](https://mlsanity.com/paper/2104.08391/) (2021)
- [Represent, Compare, and Learn: A Similarity-Aware Framework for Class-Agnostic Counting](https://mlsanity.com/paper/2203.08354/) (2022)
- [An End-to-End Transformer Model for Crowd Localization](https://mlsanity.com/paper/2202.13065/) (2022)
- [A Low-Shot Object Counting Network With Iterative Prototype Adaptation](https://mlsanity.com/paper/2211.08217/) (2022)
- [TransCrowd: weakly-supervised crowd counting with transformers](https://mlsanity.com/paper/2104.09116/) (2021)
- [Zero-shot Object Counting](https://mlsanity.com/paper/2303.02001/) (2023)
- [Few-shot Object Counting and Detection](https://mlsanity.com/paper/2207.10988/) (2022)
- [Rethinking Spatial Invariance of Convolutional Networks for Object Counting](https://mlsanity.com/paper/2206.05253/) (2022)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (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)
- [Trigger Hunting with a Topological Prior for Trojan Detection](https://mlsanity.com/paper/2110.08335/) (2021)
- [Focal Inverse Distance Transform Maps for Crowd Localization](https://mlsanity.com/paper/2102.07925/) (2021)
- [Exemplar Free Class Agnostic Counting](https://mlsanity.com/paper/2205.14212/) (2022)
- [Vision Transformer Off-the-Shelf: A Surprising Baseline for Few-Shot Class-Agnostic Counting](https://mlsanity.com/paper/2305.04440/) (2023)
- [Multi-Class Cell Detection Using Spatial Context Representation](https://mlsanity.com/paper/2110.04886/) (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)
- [CrowdDiff: Multi-hypothesis Crowd Density Estimation using Diffusion Models](https://mlsanity.com/paper/2303.12790/) (2023)
- [T-Rex: Counting by Visual Prompting](https://mlsanity.com/paper/2311.13596/) (2023)
- [DR.VIC: Decomposition and Reasoning for Video Individual Counting](https://mlsanity.com/paper/2203.12335/) (2022)
- [Counting Crowds in Bad Weather](https://mlsanity.com/paper/2306.01209/) (2023)
- [Boosting Detection in Crowd Analysis via Underutilized Output Features](https://mlsanity.com/paper/2308.16187/) (2023)
- [Video Crowd Localization with Multi-focus Gaussian Neighborhood Attention and a Large-Scale Benchmark](https://mlsanity.com/paper/2107.08645/) (2021)
- [Audio-visual Representation Learning for Anomaly Events Detection in Crowds](https://mlsanity.com/paper/2110.14862/) (2021)
- [Crowd Localization from Gaussian Mixture Scoped Knowledge and Scoped Teacher](https://mlsanity.com/paper/2206.05717/) (2022)
- [Congested Crowd Instance Localization with Dilated Convolutional Swin Transformer](https://mlsanity.com/paper/2108.00584/) (2021)
- [Coarse to Fine: Domain Adaptive Crowd Counting via Adversarial Scoring Network](https://mlsanity.com/paper/2107.12858/) (2021)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)

## Abstract (arXiv)

We address the problem of crowd localization, i.e., the prediction of dots corresponding to people in a crowded scene. Due to various challenges, a localization method is prone to spatial semantic errors, i.e., predicting multiple dots within a same person or collapsing multiple dots in a cluttered region. We propose a topological approach targeting these semantic errors. We introduce a topological constraint that teaches the model to reason about the spatial arrangement of dots. To enforce this constraint, we define a persistence loss based on the theory of persistent homology. The loss compares the topographic landscape of the likelihood map and the topology of the ground truth. Topological reasoning improves the quality of the localization algorithm especially near cluttered regions. On multiple public benchmarks, our method outperforms previous localization methods. Additionally, we demonstrate the potential of our method in improving the performance in the crowd counting task.