# Crowd Counting via Perspective-Guided Fractional-Dilation Convolution

arXiv: https://arxiv.org/abs/2107.03665 · HTML: https://mlsanity.com/paper/2107.03665/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 72 references that are in the map.
- First posted on arXiv 8 Jul 2021.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [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)
- [Switching Convolutional Neural Network for Crowd Counting](https://mlsanity.com/paper/1708.00199/) (2017)
- [Locate, Size and Count: Accurately Resolving People in Dense Crowds via Detection](https://mlsanity.com/paper/1906.07538/) (2019)
- [Point in, Box out: Beyond Counting Persons in Crowds](https://mlsanity.com/paper/1904.01333/) (2019)
- [Leveraging Unlabeled Data for Crowd Counting by Learning to Rank](https://mlsanity.com/paper/1803.03095/) (2018)
- [Crowd Counting and Density Estimation by Trellis Encoder-Decoder Network](https://mlsanity.com/paper/1903.00853/) (2019)
- [Generating High-Quality Crowd Density Maps using Contextual Pyramid CNNs](https://mlsanity.com/paper/1708.00953/) (2017)
- [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)
- [Revisiting Perspective Information for Efficient Crowd Counting](https://mlsanity.com/paper/1807.01989/) (2018)
- [Iterative Crowd Counting](https://mlsanity.com/paper/1807.09959/) (2018)
- [From Open Set to Closed Set: Counting Objects by Spatial Divide-and-Conquer](https://mlsanity.com/paper/1908.06473/) (2019)
- [ADCrowdNet: An Attention-injective Deformable Convolutional Network for Crowd Understanding](https://mlsanity.com/paper/1811.11968/) (2018)
- [Multi-Level Bottom-Top and Top-Bottom Feature Fusion for Crowd Counting](https://mlsanity.com/paper/1908.10937/) (2019)
- [Learning Spatial Awareness to Improve Crowd Counting](https://mlsanity.com/paper/1909.07057/) (2019)
- [NAS-Count: Counting-by-Density with Neural Architecture Search](https://mlsanity.com/paper/2003.00217/) (2020)
- [Counting with Focus for Free](https://mlsanity.com/paper/1903.12206/) (2019)
- [HA-CCN: Hierarchical Attention-based Crowd Counting Network](https://mlsanity.com/paper/1907.10255/) (2019)
- [Learn to Scale: Generating Multipolar Normalized Density Maps for Crowd Counting](https://mlsanity.com/paper/1907.12428/) (2019)
- [Weighing Counts: Sequential Crowd Counting by Reinforcement Learning](https://mlsanity.com/paper/2007.08260/) (2020)

## Built on by (most cited first, 15 of 15)

- [Rethinking Spatial Invariance of Convolutional Networks for Object Counting](https://mlsanity.com/paper/2206.05253/) (2022)
- [DilateFormer: Multi-Scale Dilated Transformer for Visual Recognition](https://mlsanity.com/paper/2302.01791/) (2023)
- [Redesigning Multi-Scale Neural Network for Crowd Counting](https://mlsanity.com/paper/2208.02894/) (2022)
- [Regressor-Segmenter Mutual Prompt Learning for Crowd Counting](https://mlsanity.com/paper/2312.01711/) (2023)
- [Scene-Adaptive Attention Network for Crowd Counting](https://mlsanity.com/paper/2112.15509/) (2021)
- [DAOT: Domain-Agnostically Aligned Optimal Transport for Domain-Adaptive Crowd Counting](https://mlsanity.com/paper/2308.05311/) (2023)
- [The Effectiveness of a Simplified Model Structure for Crowd Counting](https://mlsanity.com/paper/2404.07847/) (2024)
- [DenseTrack: Drone-based Crowd Tracking via Density-aware Motion-appearance Synergy](https://mlsanity.com/paper/2407.17272/) (2024)
- [An Improved Normed-Deformable Convolution for Crowd Counting](https://mlsanity.com/paper/2206.08084/) (2022)
- [Counting with Adaptive Auxiliary Learning](https://mlsanity.com/paper/2203.04061/) (2022)
- [Virtual Classification: Modulating Domain-Specific Knowledge for Multidomain Crowd Counting](https://mlsanity.com/paper/2402.03758/) (2024)
- [Reducing Capacity Gap in Knowledge Distillation with Review Mechanism for Crowd Counting](https://mlsanity.com/paper/2206.05475/) (2022)
- [Constrained Gaussian Process Motion Planning via Stein Variational Newton Inference](https://mlsanity.com/paper/2504.04936/) (2025)
- [Count2Density: Crowd Density Estimation without Location-level Annotations](https://mlsanity.com/paper/2509.03170/) (2025)
- [DenseControl: Instance-Level Controllable Synthesis of Dense Crowd Image](https://mlsanity.com/paper/2606.15592/) (2026)

## Abstract (arXiv)

Crowd counting is critical for numerous video surveillance scenarios. One of the main issues in this task is how to handle the dramatic scale variations of pedestrians caused by the perspective effect. To address this issue, this paper proposes a novel convolution neural network-based crowd counting method, termed Perspective-guided Fractional-Dilation Network (PFDNet). By modeling the continuous scale variations, the proposed PFDNet is able to select the proper fractional dilation kernels for adapting to different spatial locations. It significantly improves the flexibility of the state-of-the-arts that only consider the discrete representative scales. In addition, by avoiding the multi-scale or multi-column architecture that used in other methods, it is computationally more efficient. In practice, the proposed PFDNet is constructed by stacking multiple Perspective-guided Fractional-Dilation Convolutions (PFC) on a VGG16-BN backbone. By introducing a novel generalized dilation convolution operation, the PFC can handle fractional dilation ratios in the spatial domain under the guidance of perspective annotations, achieving continuous scales modeling of pedestrians. To deal with the problem of unavailable perspective information in some cases, we further introduce an effective perspective estimation branch to the proposed PFDNet, which can be trained in either supervised or weakly-supervised setting once the branch has been pre-trained. Extensive experiments show that the proposed PFDNet outperforms state-of-the-art methods on ShanghaiTech A, ShanghaiTech B, WorldExpo'10, UCF-QNRF, UCF_CC_50 and TRANCOS dataset, achieving MAE 53.8, 6.5, 6.8, 84.3, 205.8, and 3.06 respectively.