基于频域增强的跨域人群计数模型

doi:10.16182/j.issn1004731x.joss.25-0896

系统仿真学报 ›› 2026, Vol. 38 ›› Issue (1): 158-173.doi: 10.16182/j.issn1004731x.joss.25-0896

基于频域增强的跨域人群计数模型

张德¹^,², 梁子珊¹^,², 刘宁宁³

^1.北京建筑大学智能科学与技术学院，北京 102616
^2.北京建筑大学城市建筑超级智能技术北京市重点实验室，北京 102616
^3.对外经济贸易大学信息学院，北京 100029

收稿日期:2025-09-15 修回日期:2025-11-11 出版日期:2026-01-18 发布日期:2026-01-28
通讯作者: 刘宁宁
第一作者简介:张德(1979-)，男，副教授，博士，研究方向为计算机视觉、虚拟现实。
基金资助:
国家自然科学基金(62271035);城市建筑超级智能技术北京市重点实验室开放课题(BKL-SITUA-202502);对外经济贸易大学信息学院人工智能交叉专项

Cross-domain Crowd Counting Model Based on Frequency Domain Enhancement

Zhang De¹^,², Liang Zishan¹^,², Liu Ningning³

^1.School of Intelligence Science and Technology, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
^2.Beijing Key Laboratory of Super Intelligent Technology for Urban Architecture, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
^3.School of Information Technology and Management, University of International Business and Economics, Beijing, 100029, China

Received:2025-09-15 Revised:2025-11-11 Online:2026-01-18 Published:2026-01-28
Contact: Liu Ningning

摘要/Abstract

摘要：

人群计数以视频监控数据为输入，可应用于城市数字孪生平台建设、虚拟城市建模和智慧城市管理等领域。当应用场景与训练场景存在数据域差异时，计数性能往往显著下降，因此，提出一种基于频域增强的跨域人群计数模型。为缓解域间分布差异，构建频域特征增强模块与域不变频域适配器模块：前者利用离散余弦变换提取关键统计特征以增强空间表示能力，后者基于快速傅里叶变换分解幅度与相位谱，并通过注意力机制抑制域特异幅度信息以提取域不变特征。为应对复杂背景干扰，设计并联双注意力模块以聚焦前景区域。为解决尺度剧烈变化带来的挑战，提出多尺度特征聚合模块，实现不同尺度解码器特征的融合，从而提升模型的鲁棒性。在4个公开人群计数数据集上进行了跨域仿真实验，结果表明所提模型在大多数具有挑战性的场景中均获得最低计数误差，优于当前主流模型，可有效支撑鲁棒、高精度的人群动态仿真。

关键词: 人群计数, 频域建模, 域泛化, 仿真输入建模, 智慧城市

Abstract:

Crowd counting takes video surveillance data as input and can be applied to the construction of city digital twin platforms, virtual city modeling and smart city management, etc. However, when there are data domain differences between the application scenario and training scenario, counting performance often significantly decreases. A cross-domain crowd counting model based on frequency domain enhancement is proposed. To alleviate the distribution differences between domains, a frequency domain feature enhancement module and a domain invariant frequency domain adapter module are constructed: the former uses discrete cosine transform to extract key statistical features to enhance spatial representation ability, while the latter decomposes amplitude and phase spectra based on fast Fourier transform and suppresses domain specific amplitude information through attention mechanism to extract domain invariant features. To cope with complex background interference, a parallel dual attention module is designed to focus on the foreground region. To address the challenges posed by drastic scale changes, a multi-scale feature aggregation module is proposed to achievethe fusion of decoder features at different scales, thereby enhancing the model robustness. Cross-domain simulation experiments are conducted on four public crowd counting datasets, and the results showed that the proposed method achieved the lowest counting error in most challenging scenarios, outperforming current mainstream methods and providing effective supports for robust and high-precision crowd dynamic simulation.

Key words: crowd counting, frequency-domain modeling, domain generalization, simulation input modeling, smart city

中图分类号:

TP391.4

张德,梁子珊,刘宁宁 . 基于频域增强的跨域人群计数模型[J]. 系统仿真学报, 2026, 38(1): 158-173.

Zhang De,Liang Zishan,Liu Ningning . Cross-domain Crowd Counting Model Based on Frequency Domain Enhancement[J]. Journal of System Simulation, 2026, 38(1): 158-173.

图/表 15

图1

图2

图3

图4

表1

图5

表2

图6

表3

图7

图8

图9

表4

表5

表6

DIFA模块中超参数β的影响

$β$	SHA→SHB		SHA→UQ
$β$	MAE	MSE	MAE	MSE
0.1	18.4	31.6	214.4	495.1
0.3	19.0	28.1	159.6	276.2
0.5	12.1	21.5	124.2	222.3
0.7	19.1	27.4	158.6	272.8
0.9	23.3	34.6	224.5	629.7

表6

参考文献 33

[1]	Han Run, Qi Ran, Lu Xuequan, et al. Counting in Congested Crowd Scenes with Hierarchical Scale-aware Encoder-decoder Network[J]. Expert Systems with Applications, 2024, 238, Part D: 122087.
[2]	Chen I H, Chen Weiting, Liu Yuwei, et al. Improving Point-based Crowd Counting and Localization Based on Auxiliary Point Guidance[C]//Computer Vision – ECCV 2024. Cham: Springer Nature Switzerland, 2025: 428-444.
[3]	钟竞辉, 林育钿, 李稳强, 等. 基于数字孪生的机场人群智慧管控技术[J]. 系统仿真学报, 2024, 36(1): 27-38.
	Zhong Jinghui, Lin Yudian, Li Wenqiang, et al. Intelligent Airport Crowd Management Technology Based on Digital Twin[J]. Journal of System Simulation, 2024, 36(1): 27-38.
[4]	栾方军, 龚琪, 袁帅. 基于注意力机制和多尺度融合的人群计数网络[J]. 计算机工程, 2025, 51(3): 352-361.
	Luan Fangjun, Gong Qi, Yuan Shuai. Crowd Counting Network Based on Attention Mechanism and Multiscale Fusion[J]. Computer Engineering, 2025, 51(3): 352-361.
[5]	余鹰, 范在昌, 曾康利, 等. 渐进式认知引导的双域半监督人群计数[J]. 计算机研究与发展, 2025, 62(9): 2194-2207.
	Yu Ying, Fan Zaichang, Zeng Kangli, et al. Progressive Cognition-guided Dual-domain Semi-Supervised Crowd Counting[J]. Journal of Computer Research and Development, 2025, 62(9): 2194-2207.
[6]	Zhao Zhiyuan, Han Tao, Gao Junyu, et al. A Flow Base Bi-path Network for Cross-scene Video Crowd Understanding in Aerial View[C]//Computer Vision – ECCV 2020 Workshops. Cham: Springer International Publishing, 2020: 574-587.
[7]	Zhang Xinfeng, Han Lina, Shan Wencong, et al. A Multi-scale Feature Fusion Network with Cascaded Supervision for Cross-scene Crowd Counting[J]. IEEE Transactions on Instrumentation and Measurement, 2023, 72: 1-15.
[8]	Liu Yanbo, Hu Yingxiang, Cao Guo, et al. MGFNet: Cross-scene Crowd Counting via Multistage Gated Fusion Network[J]. Neurocomputing, 2024, 607: 128431.
[9]	Zhang Anran, Xu Jun, Luo Xiaoyan, et al. Cross-domain Attention Network for Unsupervised Domain Adaptation Crowd Counting[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2022, 32(10): 6686-6699.
[10]	Zhao Wenda, Wang Mingyue, Liu Yu, et al. Generalizable Crowd Counting via Diverse Context Style Learning[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2022, 32(8): 5399-5410.
[11]	Du Zhipeng, Deng Jiankang, Shi Miaojing. Domain-general Crowd Counting in Unseen Scenarios[C]//Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence. Palo Alto: AAAI Press, 2023: 561-570.
[12]	Liu Yuting, Wang Zheng, Shi Miaojing, et al. Towards Unsupervised Crowd Counting via Regression-detection Bi-knowledge Transfer[C]//Proceedings of the 28th ACM International Conference on Multimedia. New York: Association for Computing Machinery, 2020: 129-137.
[13]	Xu Kai, Qin Minghai, Sun Fei, et al. Learning in the Frequency Domain[C]//2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Piscataway: IEEE, 2020: 1737-1746.
[14]	Qin Zequn, Zhang Pengyi, Wu Fei, et al. FcaNet: Frequency Channel Attention Networks[C]//2021 IEEE/CVF International Conference on Computer Vision (ICCV). Piscataway: IEEE, 2021: 763-772.
[15]	Yu Xiaoyuan, Liang Yanyan, Lin Xuxin, et al. Frequency Feature Pyramid Network with Global-local Consistency Loss for Crowd-and-vehicle Counting in Congested Scenes[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(7): 9654-9664.
[16]	Shu Weibo, Wan Jia, Tan Chen, et al. Crowd Counting in the Frequency Domain[C]//2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Piscataway: IEEE, 2022: 19586-19595.
[17]	Simonyan K, Zisserman A. Very Deep Convolutional Networks for Large-scale Image Recognition[EB/OL]. (2014-09-04) [2025-08-16]. .
[18]	Zhang Yingying, Zhou Desen, Chen Siqin, et al. Single-image Crowd Counting via Multi-column Convolutional Neural Network[C]//2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Piscataway: IEEE, 2016: 589-597.
[19]	Idrees H, Tayyab M, Athrey K, et al. Composition Loss for Counting, Density Map Estimation and Localization in Dense Crowds[C]//Computer Vision – ECCV 2018. Cham: Springer International Publishing, 2018: 544-559.
[20]	Idrees H, Saleemi I, Seibert C, et al. Multi-source Multi-scale Counting in Extremely Dense Crowd Images[C]//2013 IEEE Conference on Computer Vision and Pattern Recognition. Piscataway: IEEE, 2013: 2547-2554.
[21]	Peng Zhuoxuan, Chan S H G. Single Domain Generalization for Crowd Counting[C]//2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Piscataway: IEEE, 2024: 28025-28034.
[22]	Ma Zhiheng, Wei Xing, Hong Xiaopeng, et al. Bayesian Loss for Crowd Count Estimation with Point Supervision[C]//2019 IEEE/CVF International Conference on Computer Vision (ICCV). Piscataway: IEEE, 2019: 6141-6150.
[23]	Xu Chenfeng, Qiu Kai, Fu Jianlong, et al. Learn to Scale: Generating Multipolar Normalized Density Maps for Crowd Counting[C]//2019 IEEE/CVF International Conference on Computer Vision (ICCV). Piscataway: IEEE, 2019: 8381-8389.
[24]	Wang Boyu, Liu Huidong, Samaras D, et al. Distribution Matching for Crowd Counting[C]//Proceedings of the 34th International Conference on Neural Information Processing Systems. Red Hook: Curran Associates Inc., 2020: 1595-1607.
[25]	Liu Liang, Lu Hao, Zou Hongwei, et al. Weighing Counts: Sequential Crowd Counting by Reinforcement Learning[C]//Computer Vision – ECCV 2020. Cham: Springer International Publishing, 2020: 164-181.
[26]	Deepak Babu Sam, Skand Vishwanath Peri, Mukuntha Narayanan Sundararaman, et al. Locate, Size, and Count: Accurately Resolving People in Dense Crowds via Detection[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021, 43(8): 2739-2751.
[27]	Xu Chenfeng, Liang Dingkang, Xu Yongchao, et al. AutoScale: Learning to Scale for Crowd Counting[J]. International Journal of Computer Vision, 2022, 130(2): 405-434.
[28]	Liang Dingkang, Xu Wei, Zhu Yingying, et al. Focal Inverse Distance Transform Maps for Crowd Localization[J]. IEEE Transactions on Multimedia, 2023, 25: 6040-6052.
[29]	Deepak Babu Sam, Agarwalla Abhinav, Joseph Jimmy, et al. Completely Self-supervised Crowd Counting via Distribution Matching[C]//Computer Vision – ECCV 2022. Cham: Springer Nature Switzerland, 2022: 186-204.
[30]	Chen Yuehai, Yang Jing, Chen Badong, et al. Counting Varying Density Crowds Through Density Guided Adaptive Selection CNN and Transformer Estimation[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2023, 33(3): 1055-1068.
[31]	Siddharth Singh Savner, Kanhangad Vivek. CrowdFormer: Weakly-supervised Crowd Counting with Improved Generalizability[J]. Journal of Visual Communication and Image Representation, 2023, 94: 103853.
[32]	Chen Yuehai, Wang Qingzhong, Yang Jing, et al. CSCC: Cross-scene Crowd Counting via Learning to Diversify for Domain Generalization[J]. IEEE Transactions on Multimedia, 2025, 27: 3320-3330.
[33]	Sindagi V A, Yasarla R, Patel V M. JHU-CROWD++: Large-scale Crowd Counting Dataset and a Benchmark Method[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, 44(5): 2594-2609.

方法	发表来源	SHA→SHB		SHA→UQ		SHA→UC
方法	发表来源	MAE	MSE	MAE	MSE	MAE	MSE
BL^[22]	ICCV (2019)	15.9	25.8	166.7	287.6	432.7	683.3
SPN+L2SM^[23]	ICCV (2019)	21.2	38.7	227.2	405.2	332.4	588.4
DMNet^[24]	NeurIPS (2020)	22.6	33.9	148.9	281.3	417.7	664.2
LibraNet^[25]	ECCV (2020)	11.9	20.7	127.9	204.9	—	—
RDBT^[12]	ACM MM (2020)	13.4	29.3	175.0	294.8	368.0	518.9
LSC^[26]	TPAMI (2020)	23.4	35.9	207.6	371.9	456.8	696.1
AutoScale^[27]	IJCV (2022)	23.1	39.0	—	—	—	—
FIDTM^[28]	TMM (2022)	17.4	35.1	193.6	457.9	423.1	602.5
GENet^[10]	TCSVT (2022)	14.1	24.6	184.8	371.1	333.5	504.0
CSS-CCNN++^[29]	ECCV (2022)	—	—	472.4	—	468.1	—
CTASNet^[30]	TCSVT (2023)	13.4	25.2	133.4	224.0	—	—
DCCUS^[11]	AAAI (2023)	12.6	24.6	119.4	216.6	241.8	402.2
MFFNet^[7]	TIM (2023)	12.7	30.2	142.1	271.1	323.5	482.8
CrowdFormer^[31]	JVCI (2023)	16.0	26.0	147.6	300.8	—	—
MPCount^[21]	CVPR (2024)	11.4	19.7	115.7	199.8	172.6	257.1
MGFNet^[8]	Neurocomputing (2024)	11.3	19.9	117.1	202.5	319.8	475.3
CCSC^[32]	TMM (2025)	11.7	20.8	124.5	220.9	—	—
FDE-Net	本文	12.1	21.5	124.2	222.3	184.7	370.0

方法	发表来源	SHB→SHA		SHB→UQ		SHB→UC
方法	发表来源	MAE	MSE	MAE	MSE	MAE	MSE
BL^[22]	ICCV (2019)	138.1	228.1	226.4	411.0	645.5	940.1
SPN+L2SM^[23]	ICCV (2019)	126.8	203.9	—	—	—	—
DMNet^[24]	NeurIPS (2020)	142.4	241.3	223.6	418.6	1093.9	1405.6
RDBT^[12]	ACM MM (2020)	112.2	218.2	211.3	381.9	—	—
LSC^[26]	TPAMI (2020)	153.5	250.4	279.0	490.0	731.2	1065.9
FIDTM^[28]	TMM (2022)	147.6	282.2	—	—	—	—
GENet^[10]	TCSVT (2022)	144.4	233.1	318.9	556.9	751.8	1106.1
CTASNet^[30]	TCSVT (2023)	126.9	222.3	183.8	319.2	—	—
DCCUS^[11]	AAAI (2023)	121.8	203.1	179.1	316.2	548.2	895.3
MFFNet^[7]	TIM (2023)	107.3	188.5	—	—	—	—
CrowdFormer^[31]	JVCI (2023)	121.6	208.8	304.4	586.1	—	—
MPCount^[21]	CVPR (2024)	99.6	182.9	165.6	290.4	492.8	860.9
MGFNet^[8]	Neurocomputing (2024)	105.7	183.7	176.8	307.2	631.4	927.1
CCSC^[32]	TMM (2025)	100.9	174.9	172.8	312.6	—	—
FDE-Net	本文方法	110.7	191.9	187.1	326.7	478.2	783.2

方法	发表来源	UQ→SHA		UQ→SHB		UQ→UC
方法	发表来源	MAE	MSE	MAE	MSE	MAE	MSE
BL^[22]	ICCV19	67.8	118.2	16.2	27.5	387.4	614.5
SPN+L2SM^[23]	ICCV19	73.4	119.4	—	—	—	—
DMNet^[24]	NeurIPS20	70.1	130.3	14.0	27.1	391.1	583.8
LibraNet^[25]	ECCV20	67.0	109.2	11.6	22.0	—	—
LSC^[26]	TPAMI20	97.1	154.7	12.5	21.9	535.2	822.3
GENet^[10]	TCSVT22	76.8	124.3	10.6	15.3	336.3	499.2
CTASNet^[30]	TCSVT23	68.7	118.2	12.0	23.3	278.7	445.0
DCCUS^[11]	AAAI23	67.4	112.8	12.1	20.9	143.4	224.1
CrowdFormer^[31]	JVCI23	70.8	114.9	10.3	16.0	—	—
MPCount^[21]	CVPR2024	65.5	110.1	12.3	24.1	196.7	341.2
MGFNet^[8]	Neurocomputing24	60.4	98.6	9.7	14.8	259.3	379.7
CCSC^[32]	TMM25	67.0	111.5	11.3	19.7	—	—
FDE-Net	本文方法	63.5	104.0	12.8	23.0	126.3	176.1

模块				SHA→SHB		SHA→UQ
FDFE	DIFA	MFA	PDA	MAE	MSE	MAE	MSE
				33.1	56.1	335.5	520.2
√				17.6	29.6	167.4	267.9
√	√			16.1	24.6	164.0	266.8
√	√	√		14.2	23.6	138.7	240.7
√	√	√	√	12.1	21.5	124.2	222.3

插入位置	SHA→SHB		SHA→UQ
插入位置	MAE	MSE	MAE	MSE
基线模型	33.1	56.1	335.5	520.2
Encoder1后面	25.8	35.6	165.1	268.3
Encoder2后面	18.8	29.0	157.4	286.1
Encoder3后面	14.1	26.5	138.1	241.0
Encoder4后面	14.0	29.0	147.8	262.3
Encoder5后面	17.3	25.6	208.9	325.9
Encoder3后面和Encoder4后面	12.1	21.5	124.2	222.3

基于频域增强的跨域人群计数模型

Cross-domain Crowd Counting Model Based on Frequency Domain Enhancement

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 15

参考文献 33

相关文章 3

编辑推荐

Metrics

本文评价

[1]	李欣, 刘秀, 万欣欣. 数字孪生应用及安全发展综述[J]. 系统仿真学报, 2019, 31(3): 385-392.
[2]	陈莉, 张海侠. 基于熵权-云模型的我国绿色智慧城市评价[J]. 系统仿真学报, 2019, 31(1): 136-144.
[3]	韩枫, 李晓玲, 孙秀雯, 纪凌雨. 智慧城市公共信息服务交互系统设计与实现[J]. 系统仿真学报, 2018, 30(5): 1893-1899.