# An Improved Normed-Deformable Convolution for Crowd Counting

arXiv: https://arxiv.org/abs/2206.08084 · HTML: https://mlsanity.com/paper/2206.08084/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 23 of 23)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (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)
- [NWPU-Crowd: A Large-Scale Benchmark for Crowd Counting and Localization](https://mlsanity.com/paper/2001.03360/) (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)
- [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)
- [ADCrowdNet: An Attention-injective Deformable Convolutional Network for Crowd Understanding](https://mlsanity.com/paper/1811.11968/) (2018)
- [HA-CCN: Hierarchical Attention-based Crowd Counting Network](https://mlsanity.com/paper/1907.10255/) (2019)
- [Locality-constrained Spatial Transformer Network for Video Crowd Counting](https://mlsanity.com/paper/1907.07911/) (2019)
- [A Survey of Recent Advances in CNN-based Single Image Crowd Counting and Density Estimation](https://mlsanity.com/paper/1707.01202/) (2017)
- [Spatiotemporal Modeling for Crowd Counting in Videos](https://mlsanity.com/paper/1707.07890/) (2017)
- [Crowd Counting via Perspective-Guided Fractional-Dilation Convolution](https://mlsanity.com/paper/2107.03665/) (2021)
- [Spatiotemporal Dilated Convolution with Uncertain Matching for Video-based Crowd Estimation](https://mlsanity.com/paper/2101.12439/) (2021)
- [DENet: A Universal Network for Counting Crowd with Varying Densities and Scales](https://mlsanity.com/paper/1904.08056/) (2019)

## Built on by (most cited first, 2 of 2)

- [Constrained Gaussian Process Motion Planning via Stein Variational Newton Inference](https://mlsanity.com/paper/2504.04936/) (2025)
- [DSGC-Net: A Dual-Stream Graph Convolutional Network for Crowd Counting via Feature Correlation Mining](https://mlsanity.com/paper/2509.02261/) (2025)

## Abstract (arXiv)

In recent years, crowd counting has become an important issue in computer vision. In most methods, the density maps are generated by convolving with a Gaussian kernel from the ground-truth dot maps which are marked around the center of human heads. Due to the fixed geometric structures in CNNs and indistinct head-scale information, the head features are obtained incompletely. Deformable convolution is proposed to exploit the scale-adaptive capabilities for CNN features in the heads. By learning the coordinate offsets of the sampling points, it is tractable to improve the ability to adjust the receptive field. However, the heads are not uniformly covered by the sampling points in the deformable convolution, resulting in loss of head information. To handle the non-uniformed sampling, an improved Normed-Deformable Convolution (textiti.e.,NDConv) implemented by Normed-Deformable loss (textiti.e.,NDloss) is proposed in this paper. The offsets of the sampling points which are constrained by NDloss tend to be more even. Then, the features in the heads are obtained more completely, leading to better performance. Especially, the proposed NDConv is a light-weight module which shares similar computation burden with Deformable Convolution. In the extensive experiments, our method outperforms state-of-the-art methods on ShanghaiTech A, ShanghaiTech B, UCFQNRF, and UCFCC50 dataset, achieving 61.4, 7.8, 91.2, and 167.2 MAE, respectively. The code is available at https://github.com/bingshuangzhuzi/NDConv