Haze-prior guided frequency-embedded attention learning for single-stage hazy-weather crowd counting

• Propose the haze prior guided learning process to model the haze-related knowledge. • Design a frequency-embedded attention-aggregation module for feature enhancement. • Establish a novel framework HFCC-Net for hazy-weather crowd counting task. • Generate and release two new synthesized hazy-weather crowd counting benchmarks. • Conduct extensive experiments to validate the superiority of the proposed HFCC-Net. Conventional two-stage hazy crowd counting suffers from error propagation between separate dehazing and counting pipelines, leading to degraded performance. To address this, we propose an end-to-end single-stage framework that jointly optimizes haze-invariant feature learning and crowd density estimation, achieving state-of-the-art accuracy through two key innovations. Frequency-embedded Hybrid Attention Aggregation (FHAA): This module uses frequency-domain attention to explore frequency features in hazy images, thereby enhancing key feature capture and improving feature learning. Experiments show it reduces Mean Absolute Error (MAE) by 34.48% compared to the model without it, proving its effectiveness in boosting performance. Haze-prior Guided Learning Mechanism: It explicitly models haze distortion, understands haze’s impact on images, and adaptively mitigates interference without manual dehazing annotations, reducing annotation cost and difficulty. Comparative experiments reveal a further 13.64% MAE reduction compared to the model without this mechanism, validating its anti-interference capability. The FHAA module focuses on key frequency features for crowd counting, suppressing haze noise and improving robustness in hazy weather. The haze-prior mechanism uses predicted haze distribution maps to adjust feature learning based on haze intensity, adapting to complex hazy scenes. To support research, we release two synthetic hazy crowd counting datasets at https://github.com/312524/Hazy-CC-extended . These datasets, with the same scale as Hazy-ShanghaiTechRGBD but higher haze densities, address the lack of haze-intensity diversity in existing benchmarks. Extensive ablation studies and performance comparisons on four datasets demonstrate the feasibility and superiority of our method for hazy-weather crowd counting.