# Rethinking Spatial Invariance of Convolutional Networks for Object Counting

arXiv: https://arxiv.org/abs/2206.05253 · HTML: https://mlsanity.com/paper/2206.05253/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 86 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 30 of 48)

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [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)
- [Localization in the Crowd with Topological Constraints](https://mlsanity.com/paper/2012.12482/) (2020)
- [Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds](https://mlsanity.com/paper/1909.09287/) (2019)
- [Kernel Transformer Networks for Compact Spherical Convolution](https://mlsanity.com/paper/1812.03115/) (2018)
- [Generating High-Quality Crowd Density Maps using Contextual Pyramid CNNs](https://mlsanity.com/paper/1708.00953/) (2017)
- [Cross-Modal Collaborative Representation Learning and a Large-Scale RGBT Benchmark for Crowd Counting](https://mlsanity.com/paper/2012.04529/) (2020)
- [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)
- [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)
- [AutoScale: Learning to Scale for Crowd Counting and Localization](https://mlsanity.com/paper/1912.09632/) (2019)
- [HA-CCN: Hierarchical Attention-based Crowd Counting Network](https://mlsanity.com/paper/1907.10255/) (2019)
- [Weighing Counts: Sequential Crowd Counting by Reinforcement Learning](https://mlsanity.com/paper/2007.08260/) (2020)
- [Revisiting Spatial Invariance with Low-Rank Local Connectivity](https://mlsanity.com/paper/2002.02959/) (2020)
- [Adaptive Mixture Regression Network with Local Counting Map for Crowd Counting](https://mlsanity.com/paper/2005.05776/) (2020)
- [Shallow Feature Based Dense Attention Network for Crowd Counting](https://mlsanity.com/paper/2006.09853/) (2020)
- [Cross-View Cross-Scene Multi-View Crowd Counting](https://mlsanity.com/paper/2205.01551/) (2022)
- [Learning to Count in the Crowd from Limited Labeled Data](https://mlsanity.com/paper/2007.03195/) (2020)
- [TasselNet: Counting maize tassels in the wild via local counts regression network](https://mlsanity.com/paper/1707.02290/) (2017)
- [Hybrid Graph Neural Networks for Crowd Counting](https://mlsanity.com/paper/2002.00092/) (2020)
- [Simultaneously Optimizing Weight and Quantizer of Ternary Neural Network using Truncated Gaussian Approximation](https://mlsanity.com/paper/1810.01018/) (2018)

## Built on by (most cited first, 30 of 54)

- [DAVE -- A Detect-and-Verify Paradigm for Low-Shot Counting](https://mlsanity.com/paper/2404.16622/) (2024)
- [STEERER: Resolving Scale Variations for Counting and Localization via Selective Inheritance Learning](https://mlsanity.com/paper/2308.10468/) (2023)
- [Point-Query Quadtree for Crowd Counting, Localization, and More](https://mlsanity.com/paper/2308.13814/) (2023)
- [Training-free Object Counting with Prompts](https://mlsanity.com/paper/2307.00038/) (2023)
- [Vision Transformer Off-the-Shelf: A Surprising Baseline for Few-Shot Class-Agnostic Counting](https://mlsanity.com/paper/2305.04440/) (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)
- [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)
- [OmniCount: Multi-label Object Counting with Semantic-Geometric Priors](https://mlsanity.com/paper/2403.05435/) (2024)
- [ProContEXT: Exploring Progressive Context Transformer for Tracking](https://mlsanity.com/paper/2210.15511/) (2022)
- [Counting Crowds in Bad Weather](https://mlsanity.com/paper/2306.01209/) (2023)
- [LongShortNet: Exploring Temporal and Semantic Features Fusion in Streaming Perception](https://mlsanity.com/paper/2210.15518/) (2022)
- [PoSynDA: Multi-Hypothesis Pose Synthesis Domain Adaptation for Robust 3D Human Pose Estimation](https://mlsanity.com/paper/2308.09678/) (2023)
- [AFreeCA: Annotation-Free Counting for All](https://mlsanity.com/paper/2403.04943/) (2024)
- [CountFormer: Multi-View Crowd Counting Transformer](https://mlsanity.com/paper/2407.02047/) (2024)
- [Exploring Contextual Attribute Density in Referring Expression Counting](https://mlsanity.com/paper/2503.12460/) (2025)
- [RGB-D Indiscernible Object Counting in Underwater Scenes](https://mlsanity.com/paper/2304.11677/) (2023)
- [Counting Varying Density Crowds Through Density Guided Adaptive Selection CNN and Transformer Estimation](https://mlsanity.com/paper/2206.10075/) (2022)
- [Focus for Free in Density-Based Counting](https://mlsanity.com/paper/2306.05129/) (2023)
- [Learning Discriminative Features for Crowd Counting](https://mlsanity.com/paper/2311.04509/) (2023)
- [Cross-head Supervision for Crowd Counting with Noisy Annotations](https://mlsanity.com/paper/2303.09245/) (2023)
- [FGENet: Fine-Grained Extraction Network for Congested Crowd Counting](https://mlsanity.com/paper/2401.01208/) (2024)
- [VMambaCC: A Visual State Space Model for Crowd Counting](https://mlsanity.com/paper/2405.03978/) (2024)
- [Improving Anomaly Segmentation with Multi-Granularity Cross-Domain Alignment](https://mlsanity.com/paper/2308.08696/) (2023)
- [Point-to-Region Loss for Semi-Supervised Point-Based Crowd Counting](https://mlsanity.com/paper/2505.21943/) (2025)
- [Diffusion-based Data Augmentation for Object Counting Problems](https://mlsanity.com/paper/2401.13992/) (2024)
- [Learning Spatial Similarity Distribution for Few-shot Object Counting](https://mlsanity.com/paper/2405.11770/) (2024)
- [Multi-View People Detection in Large Scenes via Supervised View-Wise Contribution Weighting](https://mlsanity.com/paper/2405.19943/) (2024)
- [Progressive Multi-resolution Loss for Crowd Counting](https://mlsanity.com/paper/2212.04127/) (2022)

## Abstract (arXiv)

Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level spatial invariance would cause overfit noise in the density map generation. In this paper, we try to use locally connected Gaussian kernels to replace the original convolution filter to estimate the spatial position in the density map. The purpose of this is to allow the feature extraction process to potentially stimulate the density map generation process to overcome the annotation noise. Inspired by previous work, we propose a low-rank approximation accompanied with translation invariance to favorably implement the approximation of massive Gaussian convolution. Our work points a new direction for follow-up research, which should investigate how to properly relax the overly strict pixel-level spatial invariance for object counting. We evaluate our methods on 4 mainstream object counting networks (i.e., MCNN, CSRNet, SANet, and ResNet-50). Extensive experiments were conducted on 7 popular benchmarks for 3 applications (i.e., crowd, vehicle, and plant counting). Experimental results show that our methods significantly outperform other state-of-the-art methods and achieve promising learning of the spatial position of objects.