Foggy Crowd Counting: Combining Physical Priors and KAN-Graph

2025-09-29

AI Summary

To address key challenges in foggy crowd counting—including target blurring, local feature degradation, and contrast attenuation—this paper proposes an end-to-end framework integrating physical modeling and data-driven learning. Methodologically: (i) a differentiable atmospheric scattering model jointly estimates dynamic transmission maps and global atmospheric light; (ii) an MSA-KAN module, inspired by the Kolmogorov–Arnold representation theorem, enhances fine-grained feature representation in degraded regions; (iii) a weather-aware graph convolutional network (GCN) dynamically captures spatial dependencies under low-visibility conditions. The core innovation lies in the synergistic optimization of physics-informed priors, nonlinear feature enhancement, and meteorology-adaptive graph structure learning. Evaluated on four foggy benchmark datasets, our method reduces mean absolute error (MAE) by 12.2%–27.5% over state-of-the-art approaches under heavy fog, significantly improving counting robustness and accuracy under complex weather conditions.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Learning to Search
• Humans and AI: Crowd Sourcing and Human Computation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Aiming at the key challenges of crowd counting in foggy environments, such as long-range target blurring, local feature degradation, and image contrast attenuation, this paper proposes a crowd-counting method with a physical a priori of atmospheric scattering, which improves crowd counting accuracy under complex meteorological conditions through the synergistic optimization of the physical mechanism and data-driven.Specifically, first, the method introduces a differentiable atmospheric scattering model and employs transmittance dynamic estimation and scattering parameter adaptive calibration techniques to accurately quantify the nonlinear attenuation laws of haze on targets with different depths of field.Secondly, the MSA-KAN was designed based on the Kolmogorov-Arnold Representation Theorem to construct a learnable edge activation function. By integrating a multi-layer progressive architecture with adaptive skip connections, it significantly enhances the model's nonlinear representation capability in feature-degraded regions, effectively suppressing feature confusion under fog interference.Finally, we further propose a weather-aware GCN that dynamically constructs spatial adjacency matrices using deep features extracted by MSA-KAN. Experiments on four public datasets demonstrate that our method achieves a 12.2%-27.5% reduction in MAE metrics compared to mainstream algorithms in dense fog scenarios.

Problem

• Addresses crowd counting challenges in foggy environments
• Quantifies haze attenuation using atmospheric scattering model
• Enhances feature representation under fog interference

Innovation

• Differentiable atmospheric scattering model for haze attenuation quantification
• MSA-KAN with learnable edge activation for nonlinear representation
• Weather-aware GCN dynamically constructs spatial adjacency matrices