## 1 Introduction  
On a clear day, capturing high-definition target images is a relatively straightforward task. However, in foggy conditions where the atmosphere acts as a turbid medium, the absorption, scattering, and reflection properties of electromagnetic waves at different wavelengths suffer severe interference from the opaque environment. This significantly deteriorates the quality of the captured images [1]. Today, how to effectively enhance the image quality captured in foggy conditions has emerged as a major focus of research and development in the field [2]. To achieve image dehazing, various methods have been proposed. Among them are computer-vision-based approaches [3, 4]. Using prior knowledge or assumptions to dehaze images, such as the dark channel prior dehazing algorithm [5, 6, 7, 8, 9]. There are also fusion-based methods that can effectively handle various turbid media [10, 11, 12]. Driven by remarkable progress in neural networks for detection and recognition tasks, researchers have increasingly adopted deep-learning-based approaches for image dehazing [13, 14, 15, 16, 17]. These methods typically operate through one of two paradigms: estimating parameters of the atmospheric scattering model via neural networks or directly generating dehazed images by training on curated datasets. But due to the fact that most of the training data for dehazing methods based on deep learning are almost synthetic datasets, when the scene changes, the restored image usually contains distortion [18]. Although the aforementioned algorithms can enhance the visibility of hazy images, they are primarily effective in light fog conditions. In dense fog, where image visibility is significantly reduced, polarization-based dehazing methods leverage additional optical information to perform haze removal. These approaches offer advantages such as algorithmic simplicity and superior dehazing capability in heavy fog [19; 20]. The polarization-based dehazing scheme was proposed by [PERSON] et al. Their method involves rotating linear polarizers to capture differential imaging of two polarized images, enabling effective haze suppression through polarization difference analysis [21]. In the subsequent development, [PERSON] et al. proposed a polarization dehazing method based on Stokes vectors, which effectively reduced noise and enhanced the dehazing ability of images [22; 23; 24; 25]. However, existing polarization-based dehazing algorithms still treat the polarization information in images as solely originating from the polarization of airlight. They rely on iterative optimization to estimate the intensity of light at infinity for enhancing polarized images. This leads to inherent limitations in certain scenarios, as polarization information in real-world scenes is jointly contributed by both atmospheric light and object radiance. Consequently, algorithms that incorporate object polarization characteristics have garnered significant attention for their potential to overcome these constraints [26; 27; 28]. In our study, we propose a fast dehazing algorithm based on polarimetric transmittance estimation that integrates target radiance polarization and airlight polarization information. By leveraging multi-scale intensity and polarization cues to accurately localize sky regions, we obtain precise estimates of atmospheric light intensity at infinity and polarization properties of airlight. Through multi-scale threshold segmentation of the scene, we distinguish between haze-occluded regions and haze-free regions, enabling spatially adaptive transmittance estimation. This approach achieves real-time haze removal while preserving critical scene details. Experimental results demonstrate that the proposed algorithm enhances image visibility significantly while maintaining maximum structural similarity (SSIM), validating its effectiveness in restoring fog-degraded imagery. The proposed algorithm enables rapid dehazing of multiple targets across diverse scenarios.